Università degli Studi di Milano
Department of Physics
Physics, Astrophysics and Applied Physics PhD School
Cicle XVIII

Relativistic Coulomb excitation ofneutron rich Fe and Ni isotopes
Academic scientific discipline :FIS/04

Author: Riccardo Avigo
Coordinator:Prof. Marco Bersanelli
Supervisors: Prof. Franco Camera
Co-Supervirsor: Dr. Oliver Wieland

Academic year 2015-2016

Commission of the final examination
Prof. Franco Camera
Prof. Zsolt Podolyack
Prof. Nasser Kalantar

Final examination
28/01/2016
Università degli Studi di Milano, Dipartimento di Fisica - Milano - Italy

Università degli Studi di Milano
Dipartimento di Fisica
Corso di Dottorato in Fisica, Astrofisica e Fisica Applicata
Ciclo XXVIII
Coordinator: Prof. Marco Bersanelli

MIUR subject: FIS/04 - FISICA NUCLEARE E SUBNUCLEARE
PACS: 25.70.Hi, 29.30.Kv, 21.10.Re

All rights reserved. No part of the publication may be reproduced in any form by print,
photoprint, microfilm or any other means without written permission from the publisher.

D/2015/10.705/3
ISBN 978-90-8649-793-5

Dissertation presented in partial
fulfilment of the requirements
for the degree of Doctor in Science.

Alla mia famiglia
To my family

Quando qualcuno ti chiede se sei un dio,
tu devi dire: si!
Ray, Ghostbusters by Ivan Reitman

Contents

Introduction

1

1

Nuclear response to E1 excitations3

1.1

E1 strength distribution in nuclei

3

1.2

Isovector Giant Dipole Resonance

4

1.2.1

Microscopic Overview

5

1.2.2

Decay Mechanism

6

Pygmy Dipole Resonance

7

1.3.1

Theoretical description

8

1.3.2

Experimental investigation

10

1.3

1.4
2

3

Low Energy E1 response in Iron and Nickel isotopes

13

Relativistic Coulomb excitation

17

2.1

Coulomb excitation

17

2.2

Relativistic energy regime

21

2.2.1

22

Eikonal approach

Experimental Setup

27

3.1

PreSPEC-AGATA setup in GSI

28

3.1.1

The magnetic FRagment Separator

29

3.1.2

The calorimeter (ToF and E-∆E) LYCCA

33

3.1.3

AGATA

37

3.2

4

3.1.4

HECTOR+

45

3.1.5

The Data AcQuisition system at GSI

47

DALI2-HECTOR+ setup in Riken

51

3.2.1

Big Radioactive IsotoPe Separator

51

3.2.2

Zero Degree Spectrometer

54

3.2.3

DALI2 and HECTOR+

55

3.2.4

The Data AcQuisition system

58

Data Analysis

61

4.1

PreSPEC-AGATA data analysis: Identification and selection of the ions

61

4.1.1

Calibration of the detectors for identification

61

4.1.2

Commissioning with isomers

62

4.1.3

Identification performance during Iron beamtime

64

4.1.4

Identification for Iron beams

67

4.2

4.3

PreSPEC-AGATA data analysis: identification and selection of reaction
products

69

4.2.1

calibration and identification

69

4.2.2

Test of consistency between FRS and LYCCA frames

72

4.2.3

Coulomb excitation selection

74

PreSPEC-AGATA data analysis: Gamma ray detection

76

4.3.1

76

4.3.2

5

AGATA
+

HECTOR80

4.4

PreSPEC-AGATA data analysis: Final Gamma ray spectra

83

4.5

DALI2-HECTOR+ data analysis: identification and selection of the ions

87

4.6

DALI2-HECTOR+ data analysis: Coulomb excitation events selection

88

4.7

DALI2-HECTOR+ data analysis: Gamma ray detection conditions

89

4.8

DALI2-HECTOR+ data analysis: Final spectra

91

Discussion of experimental results

95

5.1

Beam correlated background evaluation

95

5.2

Normalization of the cross section

98

5.3

Gamma yield contribution from GDR decay in pygmy energy region

100

5.4

Spectra subtracted and multipolarity investigation

103

5.5

E1 investigation in

5.6

Final results

70

Ni isotope

106
109

Conclusions and outlook

112

A Statistical decay in the GEMINI++ code

117

A.1 The code

117

A.2 The statistical model

118

A.2.1 The level density

118

A.2.2 The γ decay

119

B The setup simulation code
B.1 The AGATA code structure

121
121

B.1.1

Event Generator

122

B.1.2

Event Builder

122

B.1.3

Event Reconstructor

122

64,62

123

B.2 Simulations for

Fe experiment

B.3 The HECTOR-DALI code
C Femul and prespec data analysis codes

123
125

C.1 Femul

125

C.2 prespec

127

Bibliography

129

Acknowledgments

135

Introduction

This work discusses the measurement of E1 strength around one particle separation energy in the exotic neutron rich Iron and Nickel isotopes using the relativistic coulomb
excitation.
The AGATA segmented HPGe detector array, DALI2 and HECTOR+ large volume scintillator detectors have been employed for this search.
Relativistic coulomb excitation is a well established experimental technique to investigate the properties of nuclear structure: in particular it is very useful to characterize theelectric dipole response in exotic nuclei far from the stability, as it excitates mainly theE1 isovector mode.
The electric dipole response of atomic nuclei, in fact, is presently attracting large attention from the nuclear physics research community. In particular the E1 strength inneutron rich nuclei, located at around one particle separation energy (6-12 MeV energy
range) is the object of a large experimental and theoretical effort [9]. In this energy region
structures and accumulations of the E1 strength were measured in a variety of nuclei
along all the valley of stability. These structures, commonly called Pygmy Dipole Resonance (PDR) as they lie at energies below the Giant Dipole Resonance and have smaller
strength, are at the centre of the scientific debate as the strength is connected to the neutron skin thickness and the symmetry energy term of the nuclear equation of state [1], [2].
In addition, it was shown in literature that PDR, and the nuclear structure features connected with it, are relevant for astrophysics, in particular concerning neutron star structure and reactions in extreme condition scenarios [3]. The symmetry energy term of theequation of state is connected with the pressure of infinite nuclear matter, this means
1Introduction

2

that an evaluation of this parameter could provide informations on the maximum pressure sustainable by neutron stars, and therefore on their maximum dimensions. On theother hand an accumulation of strength at one particle separation energy could change
the n-γ reaction ratio in exotic environments, like supernovae, changing the production
rate of heavy nuclei.
These connections with many nuclear and astrophysics aspects, made the investigationof the E1 response of nuclei an important aspect of the recent nuclear physics research.
In spite of the large amount of data about E1 strength distribution in stable nuclei, very
few data are available for neutron rich exotic nuclei far from the stability. Two experimental campaigns to search for the pygmy dipole resonance in 64,62 Fe and 70 Ni nuclei
were recently performed. The Iron isotope investigation was performed in GSI in 2012
and concluded in 2014, during the PreSPEC – AGATA experimental campaing [4], while70

Ni E1 response was measured at the RIKEN/RIBF laboratory during the DALI2 cam-paign in autumn 2014 [5].
The response of nuclei was investigated through relativistic Coulomb excitation in inverse kinematics. This reaction mechanism coupled with the detection of the gamma
rays emitted by the excitated nuclei is a well established experimental technique to investigate nuclear properties in the energy region of PDR in nuclei far from the stability [6]. The advantage of this experimental technique relies on the predominancy of theE1 excitation at this beam velocity. Neutron rich isotopes are expected to be characterized by an enhancement of these PDR structures because of a more unbalanced neutron
over proton number ratio. There are more delocalized neutrons that in principle increase
the neutron skin thickness. The measurement of this strength is therefore an important
test bench for the theories developed to explain these structures.
In this PhD thesis, the first chapter will introduce the Giant and Pygmy Dipole Resonance modes. An overview of coulomb excitation reaction mechanism will be presented
in Chapter 2. Chapter 3 will describe the experimental setup used for the measurements
discussed in this thesis, while Chapter 4 and 5 will present and discuss the data analysis
and the results obtained.

C HAPTER 1

Nuclear response to E1 excitations

In this chapter a brief overview of the nuclear response to E1 excitation above andaround the one particle separation energy, will be presented. In the first part nuclear
giant resonances, that lie at energies around 15 MeV, will be described, while in thesecond one we will focus on the response of the nucleus around the one nucleon
separation energy. In particular this response, that is the subject of this PhD thesis, canbe interpreted as a nuclear resonance, called Pygmy Dipole Resonance (PDR). A lot of
aspects of this response need a theoretical interpretation and experimental
investigation.

1.1

E1 strength distribution in nuclei

The study of the atomic nucleus has shown in the last decades the complexity of thismany body quantum system. A lot of theoretical models have been developed to describe nuclear structure and its changes in a variatey of conditions: the nuclei show bothcollective and single particle features. Experiments with different probes are needed toinvestigate the many aspects of nuclear system. Electromagnetic interaction is a wellknown probe for nuclear features investigation thanks to the analytical description ofelectromagnetic field. As regarding dipole probes, nuclei show strength accumulations
and structures from few keVs to tens of MeV(as represented in Fig. 1.1).
In this chapter we will focus on the E1 strength function; two structures lie clearly athigh energy: the Giant Dipole Resonance (around 15 MeV) and the Pygmy Dipole Resonance (around one nucleon separation energy). The first one is characterized by a large
amount of E1 strength (almost 100% of the EWSR), while the second one represents justfew percentage of the sum rule (that is the reason of its name). Both the structures are3

1.2 Isovector Giant Dipole Resonance4

Figure 1.1: Dipole Strength distribution in the atomic nucleus. In the upper part E1 strength isdisplayed while the M1 diustribution is showed lower [8]related to significant features of nuclear structure and in the two next sections they will
be described in more detail. GDR description will be based on the discussion of Ref. [7],while PDR mainly based on the overview of Ref. [9].

1.2

Isovector Giant Dipole Resonance

Giant Resonances are collective vibrational states above the separation energy, interpreted as an harmonic vibration of the density or the shape around the equilibrium of
the nuclear system. The oscillation is defined by a small amplitude (few per cent of nuclear radius), high frequency (around 1021 Hz) and a strong damping (reflected in thelarge width of the Lorentzian associated to this vibration mode). Eq. 1.1 represnts theformula for the GDR Lorentian:σ(E) =σm Γ2m E 222 )2 + Γ2 E 2(E − Emm(1.1)

where σm is the peak cross section, Em the resonance enrgy and Γm the width that is
tipically in the range of 2.5 - 5 MeV. Giant resonances are classified according to themultipolarity: in the case of E1 excitation we are interested in an Isovector Giant Dipole
Resonance (IVGDR), characterized by ∆L = 1, ∆T = 1 and ∆S = 0. This vibration is
pictorially described in a hydrodynamical picture as an oscillation of protons in opposition of phase respect to the neutrons. The excitation can be induced by fusion reactions,charge exchange reactions, real or virtual photons. The electric field perturbates the system interacting essentially with protons, while the nuclear interaction between neutronsand protons represents the restoring force: the combined action of these two forces induces the vibration. The different Giant Resonances were investigated with different

Chapter 1: Nuclear response to E1 excitations

5

probes: this allowed to study separately each resonance. The typical Lorentzian shapein energy spectra is characterized by wide distribution (fig. 1.2) and as a consequence
the Lorentians of different Giant Resonances overlap: considerations on reaction mechanism and decay are needed to avoid contributions in the same spectrum from different
types of Resonance.
IVGDR was extensively studied since 1937: its features and beahviour in different initialconditions were investigated. Typical experimental tools were photo-absorption reactions or measurement of Compound Nucleus decay. Also heavy ion fusion reaction with
Q value sufficiently large have been used. The former allowed to scan all the lorentian
distribution, thanks to the possibility to use specific target and produce γ ray beams at
different energies via Bremsstrahlung technique, the latter allowed to populate GDRs
built on excitated states and investigate their decay.

Figure 1.2: Photoneutron cross section as a function of the energy of the excitating γs for 208 Pb [26]1.2.1

Microscopic Overview

Giant Dipole Resonances, as the other Giant Resonances of nuclei, can be described asa coherent superposition of particle-hole excitations induced by a one-body operator
acting on the ground state (eq. 1.2) or on an excitated state.
λ,σ,τ
|Ψλ,σ,τ
|Ψg.s. >GR >= O

(1.2)

where λ,σ,τ represent the multipolarity, the spin and isospin of the resonance.
In shell model picture of the Giant Resonances, the residual particle-hole interaction gen-1.2 Isovector Giant Dipole Resonance6erates a collective state formed by the coherent superposition of all particle-hole stateswith a certain multipolarity. Thanks to the fact that the residual particle-hole interaction is attractive in case of isoscalar excitation and repulsive for isovector, the isoscalar
resonances lie at lower energies than the isovector ones. Giant Dipole Resonances wereobserved in both light and heavy nuclei: in light nuclei some fragmentations occur in thelorentzian shape, while in heavy nuclei the shape is more smooth. In case of deformed
nuclei the strength is splitted and this phenomenon is interpreted as the different energy
in the oscillation along the long axis (lower energy) and along short axis (higher energy).
The excitation energy of GDR can be reproduced by the expression:
Eexc = 31.2A−1/3 + 20.6A−1/6 M eV

(1.3)

while the strength, expressed in terms of Thomas-Reiche-Kuhn (TRK) sum rule, can beobtained by:
Z Emaxσγabs dE =

Emin

60N Z
(1 + k)M eV mb
A

(1.4)

where k is a factor related to meson- exchange contribution and is a characteristic ofisovector resonances. In cases of nuclei with A > 100, in the energy range from the neutron separation energy till 25 MeV, the values of k vary from 0.1 to 0.2. Nevertheless thiscorrection factor can change significantly and it is dependant from nuclear interaction
parametyrization used for the calculations.
1.2.2

Decay Mechanism

As mentioned before, Giant Dipole Resonances are strongly damped; this is reflected in
the large resonance width (with FWHM in the range of 2.5 - 8 MeV). Giant Resonancedamping and decay is explained by different mechanisms, each of them conributes, tothe width.
Giant Dipole Resonance can be represented as a coherent superposition of 1p-1h excitation. A small contribution to the damping is due to a spreading of the strength of thiscoherent 1p-1h combination on non-collective 1p-1h states. This damping does not affectintensively the decay of GDRs in heavy ions but in light nuclei it can cause a substantial splitting. The most important contribution to damping is the coupling of this 1p-1h
excitation to more complex configurations (2h -2p excitations ...): the energy is spreadover all the degrees of freedom of the system and a compound nucleus is formed. This
damping way is usually denoted with Γ↓ (spreading width) and its contribution is themost relevant to the total width.

Chapter 1: Nuclear response to E1 excitations

7

In addition, as explained in [7], a phenomenological presciption was found for thisdamping:Γ↓ = (0.026 ± 0.005)E 1.9±0.1 M eV

(1.5)

Another damping mechanism is related to the fact that the 1p-1h coherent state is well
above the particle thresold. Therefore a significant contribution to the decay might bedue to a particle emission (depicted by Γ↑ and referred to as escape width). Also gamma
decay plays a role in the damping even if it has a little influence because the particle
γemission is favoured ( ΓΓ ≈ 10−4 ). It is important to underline that also the compound
nucleus produced by the combination of 1p-1h state with more complex states, can decay by particle emission. The contribution to the GDR width of the combination of thesetwo processes is usually represented with Γ↑↓ .
The described damping and the fact that GDRs usually lie upper than the one particle
separation energy, show that the main decay process consists in particle emission, in particular neutron emission. For this reason, E1 strength distribution in this energy regionis studied via photoabsorption and neutron emission reaction. The relation
σ(γ) =Xσ(γ, xn)(1.6)

xexhausts all the photoabsorption cross section with good approximation.

1.3

Pygmy Dipole Resonance

The E1 strength distribution of atomic nuclei is almost completely exhausted by Giant
Dipole Resonance (as shown in Fig. 1.1). A small fraction of this strength is locate around
one particle separation energy and it is called Pygmy Dipole Resonance. These states
have shown a double nature. Experimental investigation (as in [31]) pointed out thatthey can be excitated with both isoscalar and isovector probes.
In the last decades the strength accumulation, here discussed, attracted the interest of
the scientific community, not only for the implications in nuclear structure, but also for
the important correlations in other fields. In neutron rich nuclei it was shown that thisamount of strength is proportional to the ”neutron skin thickness” [22], [2]. Nuclei with
N>>Z show a core with an equal number of neutrons and protons while the neutrons
in excess form an external shell (called neutron skin). It was proved that a correlation
between the strength of the PDR and the depth of this netron crust [3]. This thickness wasestimated as the difference between the radius of neutron density function and the radiusof the proton one. As shown in (Fig. 1.3) the Pygmy Dipole Resonance is described as an1.3 Pygmy Dipole Resonance8

oscillation of this neutron skin against the core. This interpretation is still under debate,also Toroidal modes are considered in literature to explain the lower energy states [32].
In addition the level of collectivity of this state is not fixed yet, for this reason many
articles refer to this state as Pygmy Dipole Strength. On the other hand it was uderlinedthat these states are also connected with the simmetry energy term in nuclear Equation
Of State (EOS) [2]. The strength is proprtional to the slope of simmetry energy term
evaluated at saturation density. This parameter is strictly connected with the thicknessof the neutron skin, the compressibility of the nuclear matter and the pressure of pureneutron matter. Dependances from these nuclear features were shown also in the dipole
polarizability [25]αD =~c
2π 2 e2

Z

σγ
dω
ω2

(1.7)

where σγ is the photo-absorption cross section.
The estimation of this quantity is based on the measurement of E1 strength distributionof the nucleus. Even if the relation with the nuclear structure properties is not as strict
as in PDR case, this method does not require a disentanglement of PDR strength from
GDR tail.
The nuclear structure aspects, here discussed, are also relevant in neutron star models;
they influence the dimension extimations and, as a consequence, the radius of neutronstars. In particular the pressure of pure neutron matter plays a key role in this extimation
because it supports neutron stars against gravitational collapse [3]. Another astrophysical aspect connected with this strength at one particle separation energy is the isotope
aboundance in stars. In fact it was shown that the aboundances of heavy nuclei in thestars is higher than expected [23]. One of the aspects that could explain this disagreement is related to the fact that the presence of this strength in nuclei could change then-γ, γ-n reaction rate in extreme astrophysics environments like supernovae. This phenomenon could have the consequence to change the rate of the photon break down ofheavy nuclei and the effect would be an enhancement of heavy isotopes [24].
1.3.1

Theoretical description

In spite of the fact that the first experimental evidences of an enhanchement of gamma
ray strength around 5-7 MeV were obtained in early 60s [10], the first theoretical model
was proposed in 1971 by R. Mohan, M. Danos and L.C. Biedernhan [11]. It consisted ina qualitative three-fluid hydrodinamical description of the interaction between neutronsand protons in neutron rich nuclei, showing two dipole modes: the Giant Dipole Reso-Chapter 1: Nuclear response to E1 excitations

9

Figure 1.3: Pictorial description of the PDR macroscopic interpratation. In neutron rich nuclei,
neutron in excess form a skin around a core with N=Z. PDR is interpreted as the oscillation of thisskin (the blue shadow) against the core (purple sphere).

nance and another one at lower energy and two orders of magnitude weaker.
This delay in theoretical description shows how the microscopic model calculations for
low-lying E1 strength are still a challenging task. While IVGDR, the gross feature of the
E1 response, is described consistently in many models, the low energy structure differs
more drastically between different calculations, showing a dependence on the propertiesof the nuclear force not fully fixed yet.
In recent years different approaches were explored: Hartree–Fock and Hartree–Fock–Bogoliubov
plus (quasi-particle) Random Phase Approximations (Q)RPA based on a variety of interactions [2], second RPA calculations [12], the quasi-particle phonon model (QPM) including complex configuration [13], the extended theory of finite Fermi systems (ETFFS) [14],the Landau–Vlasov equations [15], the relativistic RPA or QRPA [16], the relativistic
quasi-particle time-blocking approximation [30], and the algebraic Interacting Boson
Model [18]. In almost all these calculations the low lying E1 strength was observed but
the degree of collectivity is still under debate. Moreover even if different modes werediscussed, many of these models show that this strength is a signature of a neutronskin oscillation. Also the theoretical dependence of the magnitude of the strength by theasymmetry parameter α=(N-Z)/A was reproduced by both experimental data [1] andtheoretical calculations (as shown in Fig. 1.4).
Approaches based on covariant energy density functionals were proved to be succesful
tools for investigating low-lying E1 strength, in particular the fully self-consistent relativistic quasiparticle random-phase approximation (RQRPA) [19] (as shown in Fig. 1.5).
This approach was supplemented with the coupling to low lying vibrations within therelativistic quasiparticle time blocking approximation (RQTBA) in a fully consistent way
that enables to reproduce the fragmentation of the giant dipole resonance as well as of
the PDR and to describe the dipole strength of the low-energy part of the spectrum. The

1.3 Pygmy Dipole Resonance

10

Figure 1.4: Left panel: PDR strength in the Sn isotopic chain as a function of the neutrons number.
The two data set are obtained with RQRPA and RQTBA approaches. Right panel: PDR strength in
the Sn,Ni and Pb isotopes as a function of the squared asymmetry parameter α [20].

main improvement of this last approach is the reproduction of the fragmentation of thestrength of the few low-lying states in the RQRPA. The fact that this higher density was
obtained with the coupling to complex configurations, seems to be a step towards a more
realistic description of the E1 response of the nuclei in this energy region.
1.3.2

Experimental investigation

The interest of scientific community in this subject and the double nature (isoscalar andisovector) of these states has motivated the experimental investigation with different
probes and experimental techniques. Indeed after forty years of experiments an exahustive description of the pygmy dipole states is not avaible yet. A brief resume of the effort
to measure the features of these states is presented here.
The first method applied to investigate PDR in stable nuclei was Nuclear Resonance Fluorescence (NRF). In particular (γ,γ’) reactions provided a lot of data on stable nuclei inthe energy region below the binding energy. The high selectivity to dipole-states, thewell known excitation mechanism and the possibility to use HPGe detector in measuring de-excitation gamma rays allow to obtain high precise measurements of both energy
and strength for dipole states below one particle separation energy.
As introduced in previous section, the interesting energy region for PDR extends alsoChapter 1: Nuclear response to E1 excitations

11

Figure 1.5: Proton and neutron transition densities for two pronounced peaks at low excitation energy (8.94 MeV and 11.78 MeV) for 116 Sn. In the last panel GDR transition densities as comparison.
All the transition densities plotted were obtained with RQRPA approach [20], [21].

above the binding energy. In order to investigate also this energy range, photo-dissociation
experiments were performed. The critical point was the fact that neutrons emitted in (γ,n) reactions do not have all the energy of the state because daughter nuclei have often
low energy excitated states. The introduction of Bremsstrahlung technique for gamma
ray production allowed to investigate PDR in a large excitation energy region thanks
to the continuous spectrum of gamma rays colliding on target. These two techniqueprovided a lot of informations about nuclei along all the valley of stability. Also othertechniques with real photons were applied, as tagged photons and laser Compton backscattering.
The limit of these approaches is represented by the fact that only PDR in stable nuclei
can be investigated; in addition just the isovector character is observed while they cannot provide any information on isoscalar aspects accessible only with nuclear probes.
Coulomb excitation provided a technique to have the access also to exotic nuclei. The
possibility to excitate heavy-medium nuclei by virtual photon is connected with highresolution ion tracking: it is essential to recontruct ion tracks to select pure coulomb interaction events. In addition even if at relativistic energies dipole excitation dominates12

1.3 Pygmy Dipole Resonance

Figure 1.6: Schematic view of LAND setup. Sn radioactive isotope beam is investigate via virtual photon break-up. Crystal Ball array allow γ detection; ALADIN magnet separates reaction
products, charge particles and neutrons; LAND array counts decay neutrons emitted [27].

on other multipolarities, for highly precise measurements these contributions has to beconsidered. For this reason highly precise particle detectors are needed to measure energy and momentum of reaction products. It is necessary to use gamma ray detector
systems that cover an angular range sufficiently wide to fix the multipolarity of gamma
rays emitted in the de-excitation. The key point of this technique is that it can be applied also in inverse kinematics: this implies that exotic nuclei with short lifetime can beinvestigated, thanks to the accessibility of radioactictive ion beams. Similar method isused in investigating exotic nuclei with virtual photon break-up technique (Fig.1.6). A
radioactive beam is brought to collide with a high Z value target to induce the break up
via coulomb excitation. Then all the γ rays, emitted neutrons and fragments are detected
to reconstruct the excitation energy of the incident exotic ions. The investigation of PDR
is based on the measurement of neutrons emitted. Due to scarce neutron detection efficiency of neutron counters and threshold effects at one particle separation energy, thismeasurements requires accurate simulation of the experimental setup.
The double nature of PDR (isoscalar and isovector) requires an investigation not onlywith electromagnetic probes, that are sensitive to isovector character, but also hadronicinteractions [31]. Typical experimenthal techniques consist in inelastic scattering with αChapter 1: Nuclear response to E1 excitations

13

particles at some tens MeV/u. An awkward aspect of isoscalar interaction is the low selectivity in multipolarity. For this reason it is important to measure not only α scatteredparticles but also the γ decay. An experimental setup able to provide both these measurements allows to select dipole excitation, reducing the contamination from higher
multipolarities.

1.4

Low Energy E1 response in Iron and Nickel isotopes

As explained in the previous section, the low energy E1 response of nuclei is actuallyobject of experimental and theoretical investigations. Pygmy states, as GDR states, show
splitting in tiny substructers around one particle separation energy. In this thesis thesesubstructures will be investigated in 62,64 Fe and 70 Ni. It is important to underline that
this investigation has not yet been performed in nuclei far from the stability with highenergy resolution. Indeed the B(E1) values of the states next to one particle separationenergy were already measured for stable neutron rich isotopes as shown in fig.1.7. The

Figure 1.7: Summed B(E1) values versus neutron to proton ratio [28].

mass region considered in the measurements discussed in this thesis was chosen to bearound 68 Ni: this nucleus was already studied both on the theoretical and experimental
point of view. In particular the Pygmy Strength was measured by Milano group withthe relativistic coulomb excitation [6], and also by LAND group with the photon breakup technique [29]. The measurements here discussed will provide information on the14

1.4 Low Energy E1 response in Iron and Nickel isotopes

evolution of the low energy tail of this dipole strength at varying of proton and neutron
numbers in an exotic mass region, going from an even-even spherical nucleus to a more
deformed (62,64 Fe) nuclei and, in the case of 70 Ni, adding two neutrons. Theoretical
calculations performed with Relativistic Quasiparticle Random Phase Approximation(RQRPA), Relativistic Quasiparticle Time Blocking Approximation (RQTBA) and a Relativistic Quasiparticle Time Blocking Approximation version with 2q⊗phonon (RQTBA2) are shown in fig. 1.8 . It is possible to see how the distribution of these states change

Figure 1.8: Low energy dipole spectrum of 68,70,72 Ni calculated with the RQRPA (black dottedlines), RQTBA (blue dashed lines), and RQTBA-2 (red solid lines) with a smearing parameter of
200 keV. The arrows indicate the neutron thresholds [30].

with the neutron number. Calculations using RPA approach were performed also for
the Iron isotopes (fig.1.9). In this case it is possible to see clearly the increase of pygmy
strength as the neutron number increases.

Chapter 1: Nuclear response to E1 excitations

15

Figure 1.9: Energy dipole spectrum of 56,62,64 Fe calculated with the RPA approach (for courtesyof prof. Roca Maza).

C HAPTER 2

Relativistic Coulomb excitation

The pygmy dipole strength investigation, described in this thesis, was performed withthe well established relativistic coulomb excitation technique. Coulomb excitation is areaction of inelastic scattering between two nuclei in which part of the kinetik energy istransferred from one to the other through their electromagnetic field. The goodknowledge of the electromagnetic interaction, the possibility to obtain the reduced
probabilities and the multipolarity for the nuclear transitions makes this reaction
mechanism one of the most used to investigate the nuclear structure. In this chapter abrief theoretical review (based on the review by Bertulani [33]) of this experimental
technique will be presented, focusing on the particular conditions in which theexperiments here discussed took place.

2.1

Coulomb excitation

In Coulomb excitation reactions the nuclei are excitated through the exchange of virtual photons between the projectile and target. The electrostatic potential of a system ofpoint-like charges can be written as:
V (r) =

Xiei|r − ri |(2.1)

This potential can be rewritten using the multipole expansion:
V (r) =

XLM

4π
1Y ∗ (n)M(EL, M )2L + 1 rL+1 LM(2.2)

where n is the direction of vector r and M(EL, M ) is the electric multipole moment. If
we consider a charge distribution instead of a system of point-like charges, the electric172.1 Coulomb excitation

18

multipole moment can be expressed using the charge density operator:Zr
M(EL, M ) = d3 rρ(r)rL YLM (n) with n =
r

(2.3)

For a radiative transition in a nucleus i → f, where i indicates the initial and f the final
state, it is possible to define the reduced transition probability as:
B(EL; i → f) =X

2

(M(EL, M ))f i

(2.4)

M Mf

or, using the reduced matrix element:
B(EL; i → f) =1
2
|hf kM(EL, M )k ii|
2Ji + 1

(2.5)

This relation has the advantage of being independent by the projections on Mi . The same
quantity can be easily obtained for the inverse transition:
B(EL; f → i) =2Ji + 1
B(EL; i → f)
2Jf + 1

(2.6)

For example in the case represented in fig. 2.1, the equation 2.6 becomes:
B(E2; f → i) =2·0+1
B(E2; i → f)
2·2+1

(2.7)

As a consequence the B(E2) value for the excitation:
B(E2; i → f) = 5B(E2; f → i)

(2.8)

Figure 2.1: The figure represents an example of an excitation from an initial 0+ level to a final 2+

Rutherford scattering (Fig 2.2) provides a classical description of Coulomb interaction between a target with a charge Z2 and a projectile with a charge Z1 moving withrespect to the target. On the basis of this description, a semi-classical treatment is avaible

Chapter 2: Relativistic Coulomb excitation

19

Figure 2.2: The figure represents the classical situation of Rutherford scattering. A projectile withcharge Z1 , and velocity v is moving respect to a target with charge Z2 . The scattering is characterized by an impact parameter b and an angle of scattering θ, while φ is the angular position of the
projectile respect the target during the interaction.

and it is valid for almost all the cases of low beam energy [34] (Ebeam ¡50MeV/u). In the
not relativistic case the interaction hamiltonian for the excitation can be written as:Zρch (r1 − R1 )ρch
Z1 Z2 e2
2 (r2 − R2 )H 0 = d3 r1 d3 r2 1−
(2.9)
|r1 − r2 |R(t)The interaction between the two nuclei as the point like particle is subtracted because
it determines the trajectory and not the excitation. In order to semplify the expressions
we require that only the target nucles is excitated and we consider the projectile like apoint-like charge ρch
2 (r2 − R2 ) ≈ Z2 eδ(r2 − R2 ). In the center of mass frame the multipole
expansion allows to write:
H 0 = Z2 e

X
L>0,M

1
4π
Y ∗ (R(t))M(EL, M )2L + 1 RL+1 (t) LM(2.10)

It is possible to demonstrate [36] that the transition amplitude for excitation i → f isZi ∞af i = −dtHf0 i (t)eiωt(2.11)~ −∞The reaction rate will be obtained summing this amplitude over all the projections.
X
1
2
wf i =|af i |
(2.12)
2Ji + 1
Mf Mi

The trajectory influences the interaction via the integral:Z ∞1∗
ILM (ω) =dt L+1 YLM(R(t))eiωt
R(t)−∞
this contribution appears in the cross section as a function of the multipolarity:2
dσf i (L)πZ2 eaB(EL; i → f) X
2=
|ILM (ωf i )|3dΩ
~sin2 (θ/2)(2L + 1)M

(2.13)(2.14)

2.1 Coulomb excitation

20

where a is the closest distance reached by the projectile.
If also magnetic interactions are cosidered, the scalar and vector potentials, generated by
the projectile with charge Zp , have to be used in the hamiltonian.
Z ∞
1
dt
eiωt
φ(ω, r) = Zp e|r−r0 (t)|−∞A(ω, r) =

Z ∞

Zp e
c

v0 (t)eiωt

−∞

1
dt
|r − r0 (t)|(2.15)(2.16)

This allows to obtain a more complete evaluation of the cross-section distribution:dσi→f
4π 2 ZP 2 e2 2 4 X B(πL, Ii → If )2=
a0 |S(πL, M )|dΩ~2
(2L + 1)3

(2.17)

πLM

where

s
=

1+

b2
a20

(2.18)

considering that π = E or M andZ ∞r0−L−1 (t)YLM θ0 (t), φ0 (t)eiωt dt(2.19)

50 {r0−L−1 (t) × YLM [θ0 (t), φ0 (t)]}eiωt dt(2.20)

S(EL, M ) =−∞S(M L, M ) = −

1
L0 ·
Lm0 c

Z ∞
−∞

It is possible to evaluate the Coulomb cross section per solid angle as:
X Z dσi→fdσC=
ρf (Eγ )dEγdΩdΩ(2.21)

f

Where ρf (Eγ ) is the density final states in the target nucleus. Using 2.17 we obtain:
X Z dEγ dnπL
dσC=
(Eγ )σγπL (Eγ )(2.22)dΩEγ dΩ
πLwhere σγπL is the photoabsorption cross section of the nucleus at a fixed multipolarity.
The two quantities used for this evaluation, the photoabsorption cross section and thenumber of virtual photons dnΩπL exchanged between the target and the projectile, can beobtained using the following relations:
σγπL (Eγ ) =(2π)3 (L + 1) X
ρf (Eγ )L[(2L + 1)!!]2



f

Eγ
~c

2(L−1)B(πL, Ii → If )X
Zp2 α L[(2L + 1)!!]2
c2 a20 4dnπL=|S(πL, M )|dΩ
2π (L + 1)(2L + 1)3 Eγ 2(L−1)~cM(2.23)(2.24)

Chapter 2: Relativistic Coulomb excitation

21

The angular dependence can be rewritten in terms of dependence from impact parameter because it is related to the scattering angle. For this reason the Coulomb cross section
can be expressed as:
X
dσC
=
2πbdb

Z

πL

dEγ
nπL (Eγ , b)σγπL (Eγ )Eγ(2.25)In order to obtain total Coulomb cross section, we need to integrate from a minimum impact parameter. The same result can be obtained integrating till a maximum scattering
angle θmax . This is essential at high beam energy (Ebeam ¿50MeV/u) where also nuclear
excitation can have a strong role. As a consequence the number of virtual photons becomes:

Z θmaxdnπL(2.26)dΩ0
When kinetic energy of projectile increases, the number of virtual photons at highNπL (Eγ ) = 2πdθsinθ

energy increase and in this way it is possible to access to high energy excitation state of
the target (as in Fig 2.3).

Figure 2.3: Calculated cross sections for intermediate-energy Coulomb excitation at different beamenergies for a 40 S projectile impinging on a gold target [35]2.2

Relativistic energy regime

If we consider a relativistic beam, the electromagnetic field in the target nucleus centerof mass frame (considering that the projectile moves along z-axis) has to be expressed2.2 Relativistic energy regime22

as:φ(r, t) = q

γZe
2

2

(2.27)(x − b) + y 2 + γ 2 (z − vt)

where b is the x-coordinate of the projectile trajectory, andA(r, t) =v
φ(r, t)c(2.28)

Using a procedure similar to the one used for the general sitaution, and through somelong calculations but straightforward [37] we obtain the Coulomb cross section as:X
X Z dEγσC =σπL =NπL (Eγ )σγπL (Eγ )(2.29)EγπLπL

In the case of E1 excitation we have:
2Z 2 α  c 2
v2 ξ2 22NE1 (Eγ ) =(K1 − K0 )
ξK0 K1 −πv
2c2(2.30)

where the modified Bessel functions KM are functions of ξ(R) = ωRγv with R as the distance of closest approach.
The spectrum of the virtual photons exchanged in a collision, shows a kind of cutoff at
an energy that depends on the impact parameter. In particular (as in Fig 2.4) the numberof virtual photons exchanged is considered to fall down approximately at:
Eγmax '

γ~vb(2.31)

which is called adiabatic cutoff energy. This value it is obtained via an interpolation of
the virtual photon spectrum. This means that the spectrum does not stop at the cutoff,
but the contribution at higher energies are considered small.
Scattering at relativistic beam enery requires a more complex quantum approach dueto the fact that both coulomb and nuclear fields have a not-negligible role in the interaction. Thanks to the fact that scattering at these energies satisfies the hypotesis of eikonal
approach, calculations are achieved in a simple manner.
2.2.1

Eikonal approach

The Eikonal(straigth line) approximation requires that a projectile with a kinetic energy
in the laboratory frame E lose in the target a small energy ∆E to satisfy the relation∆E/Elab  1; as a consequence the scattering angle θ is very small (θ  1). Under theseChapter 2: Relativistic Coulomb excitation

23

Figure 2.4: Energy spectrum of virtual photons, per unit of area, exchanged in a collision between
208Pb and 16O at 100 MeV/nucleon and with impact parameter b=15 fm [33]conditions we can write the free-particle wave function, for a projectile colliding on atarget as:
ψ(r) = eikz φ(z, b)(2.32)

assuming that r = (z, b), where the z axis represents the beam direction. According
to the Distorted Wave approximation, the scattering due to a potential V (r) induces a
distortion in the free-particle wave function. The outcoming waves can be computed(after a partial wave-expansion) solving the Schrodinger Equation:

 2
d
2
+
k
(r)
χl (r) = 0
l
dr2
with

kl (r) =1/2
l(l + 1)~2
2µ
E
−
V
(r)
−
~2
2µr2

(2.33)(2.34)

If we assume that the function φ varies slowly with respect to z and b we obtain:∇2 φ  k |∇φ|(2.35)

Neglecting 2nd and 3rd order terms, equation 2.33 in cylindrical coordinates becomes:∂φi= − V (r)φ∂z~v

(2.36)

ψ(r) = eikz+iχ(b,z)(2.37)The solutions of this equation are:

2.2 Relativistic energy regime

24

where
χ(b, z) = −

1
~v

Z z

V (b, z 0 )dz 0(2.38)−∞

is called the ”eikonal phase”.
(−)

(+)

Depicting Φk’ (r) and Φk (r) the incoming and outcoming distorted waves, in the center of mass frame, (2.37) allows to write this as:
(−)

(+)

Φk’ (r)Φk (r) = eiqr+iχ(b,z)(2.39)

with q = k’ − k. The eikonal phase can be expressed as a sum of two contributions:Z ∞1
χ(b) = −U opt (z 0 , b)dz 0 + iχC (b)(2.40)~v −∞ N
opt
where UNis the nuclear optical potential andχC (b) =2Zp Zt e2ln(kb)~v(2.41)

is called ”Coulomb eikonal phase” and Zp and Zt are the charges of respectively the
projectile and the target.
This result can be used to write the inelastic scattering amplitude in a easier way. In
particular if we assume that the interaction potential is purely Coulombian, after themultipole expansion we obtain:c
Zek X M  w L √i
hIf Mf | M(πL, −M ) |Ii Mi i
2L + 1e−iM φ ΩM (q)GπLM
fC (θ) = i
γ~v
c
v
πLM
(2.42)
GπLM are analytical functions for electric and magnetic field multipolarities, and ΩM (q)is:Z ∞ΩM (q) =
dbbJM (qb)KM

0

wb
γv



eiχ(b)(2.43)

where q is the momentum transfer (q = 2ksin(θ/2)), while scattering angles are represented by θ and φ.
On the basis of these results and using the same procedure discussed in the previous
section, it is possible to obtain:
1 X dnπL πL
d2 σC(Eγ ) =σ (Eγ )
dΩdEγ
Eγ
dΩ γ

(2.44)

πL

πL
where dndΩ
is the virtual photon number per solid angle

dnπL= Z 2α
dΩ



ωk
γv

2

L[(2L + 1)!!]2 X
2
2|GπLM | |ΩM (q)|(2π)3 (L + 1)M

(2.45)

Chapter 2: Relativistic Coulomb excitation

25

On the basis of the Eikonal approximation hypotesis we can consider dΩ ' 2πqdq/k 2 ; inaddition the closure relation for Bessel functions allows to obtain the following expression of Coulomb cross section:dσC
1 X(Eγ ) =NπL (Eγ )σγπL (Eγ )dEγ
Eγ(2.46)

πL

where NπL (Eγ ) is the total number of virtual photons. This contribution can be evaluated as:
NπL (ω) = Z 2 α



ωk
γv

with

2

L[(2L + 1)!!]2 X
2|GπLM | gM (ω)(2π)3 (L + 1) m

2 Z
 
ωb −2χI (b)
w
2
dbbKM
e
γv
γv
In this relation χI (b) is the imaginary part of χ(b) (Eq. 2.40).

(2.47)

gM (ω) = 2π

(2.48)The theory of Coulomb excitation described in this chapter has shown the dependencesof the Coulomb cross section by the states under invetigation: in particular through thenuclear structure B(Eλ) value. In experiments here discussed, these dependences will
be exploited to collect informations on the pygmy states, subject of this PhD thesis. Fig.
2.5 shows the spectrum of virtual photons calculated for the experiments here
discussed and the trend expected for the cross section of the first 2+ level excitation and
GDR excitation.

Figure 2.5: Left panel: energy spectrum of total number of virtual photons calculated for theexperiments discussed in this thesis. Right panel: evaluation of the cross section of the first 2+
level and GDR excitation for one of the measurements introduced in the next chapters.

Radiative γ decay after Coulomb excitation was measured. The number of the γsdetected during the experiment can be obtained by the simple formula:Nγ = σ c NT NB 

(2.49)

26

2.2 Relativistic energy regime

where NT is the number of scattering centres (target atoms),NB is the number ofprojectiles and  is the detection efficiency of the system. The statistics collected allowes
to access to the Coulomb cross section and through this quantity, to the B(E1) value
associated to the pygmy states.

C HAPTER 3

Experimental Setup

The investigation described in this work is about an experimental campaign on 62,64 Fe
performed at GSI during PreSPEC-AGATA campaign (2012-2014) and on 70 Ni
performed at Riken laboratories during the DALI2-HECTOR+ campaign (autumn
2014).
The dipole E1 response of neutron rich 62,64 Fe nuclei in an energy range from 6 to 10
MeV has been measured, while in 70 Ni case the acquired statistics allows to extends theenergy range to 16 MeV. The exotic nuclei were produced and separated in flight at
relativistic energies. Iron isotopes were produced at GSI FRS facility by thefragmentation of a 700 AMeV primary 86 Kr beam on a 9 Be target (2.5 g/cm2 ). 70 Ni was
obtained by fission of 238 U at RIKEN RIBF facility.
The beam cocktail of the products from the primary beam reaction was filtered andidentified with a magnetic separator and brought to collide on a secondary target tomeasure the gamma decay of the projectile excitation. In case of Iron isotopes FRS
magnetic separator provided the selection of the nuclei of interest. In 64 Fe measurement
the exotic beam was made to collide at ∼400 AMeV on a thick lead target (1g/cm2 ),while 62 Fe was made to collide over a thick gold target (2g/cm2 ). In Riken the selectionof 70 Ni was obtained with Big-Rips separator and the beam collided on the same gold
target (2g/cm2 ) as for the 62 Fe at 260 AMev.
At GSI the gamma ray detector system used was the AGATA array coupled with
HECTOR+. AGATA [64] is an array of HPGe detectors electronically segmented while
HECTOR+ is an array of large volume LaBr3 :Ce and BaF2 scintillator detectors [58]. In
Riken the DALI2 [5] array was coupled with eight LaBr3 :Ce detectors from HECTOR+
array. DALI2 is an array made by 180 NaI scintillator detectors organized in a particularconfiguration to maximize the efficiency and minimize the doppler broadening [5].
27

3.1 PreSPEC-AGATA setup in GSI

28

The selection and determination of the products of reaction on secondary target isneeded to select coulomb excitation events. At GSI this selection was provided by the
LYCCA array [59]. It consists in a system of silicon striped detectors (DSSSD) for ion
tracking, plastic scintillators for time of flight estimation and a wall of E-∆E telescopes
made by thin silicon detectors coupled with thick CsI scintillators. In Riken ZDS
magnetic separator provides the identification and selection after the secondary target.
In this chapter the two experimental setups and their performances will be described.
An overview of the two data acquisition systems, NARVAL coupled with MBS for GSI
and RIBFDAQ for Riken, will be presented and in addition the trigger conditions will
be explained.

3.1

PreSPEC-AGATA setup in GSIThe GSI facility was able to provide radioactive ion beams for the nuclear structure investigation. The improvement of detector systems for γ spectroscopy and for ion detection allowed to measure fine structures also in exotic nuclei. The experimental setup
PreSPEC was prepared to couple the availability of rare isotope beams with the mostaccurate detector systems, concerning the γ detection it is actually the AGATA array.

Figure 3.1: PreSPEC - AGATA setup (HECTOR+ ) [4]The radioactive ion beams are produced from a stable primary beam through its interaction with a Beryllium target: the products of the induced reactions form a cocktail beam. The magnetic separator FRS (FRagment Separator) allows the identificationand selection of the rare ion beam of interest. This secondary beam is brought to imping on a secondary target where reactions of interest take place. The reaction productsChapter 3: Experimental Setup

29

identification and the measurement of the trajectory of the incoming and outcoming
beam from the target are performed with the calorimeter LYCCA(Lund-York-Cologne
CAlorimeter). The γ detection was provided by the HPGe detector array AGATA (Advance GAmma Tracking Array) which was coupled with the HECTOR+, array of LaBr3 :Ceand BaF2 scintillator detectors. In the next sections every apparatus will be described indetail.

3.1.1

The magnetic FRagment Separator

FRS is an in-flight magnetic spectrometer used to select radioactive isotope beams from astable primary beam. The synchrotron SIS can accelerate stable beams from Hydrogen to
Uranium up to 1-4.5 AGeV [60]. The beam is iniected in FRS beam line and impings on a
production target where fragmentation or fission reactions occur and produce a cocktail
beam with the reaction products. The technique exploited to identify and separate theions in the cocktail beam is the Bρ − ∆E − Bρ method. The spectrometer consists of fourstages referred to as S1, S2, S3 and S4. Each stage is made up of five quadrupoles, a ±30odipole magnet and a pair of sextupoles. The dipole magnets are used to separate andidentify the ions while the quadrupole magnets are used for both illuminate the field
volume of the bending magnets and also focusing the beam on the focal planes (denoted
as F1, F2, F3, F4). Higher order aberrations are corrected by sextupoles. This magnet
system allows to have an high resolution spectrometer. The incoming beam is analyzed
evaluating the magnetic rigidity and the time of flight; these two quantities allow todefine the A/Q ratio of the ions. A profiled degrader is used on one hand to reduce theemittance of the beam and on the other hand to improve the separation of the ions. In
2fact the energy loss of an ion in matter scales as: ∼ MZv2 and therefore the ∆E loss in the
degrader depends on proton and mass number of the ion. The degrader can be shaped
according two operational modes : achromatic and monoenergetic mode. The highest
resolving power is obtained with achromatic mode. The term achromatic means that thehorizontal position and angle of a particle at the last focal plane (F4) does not dependon its momentum. The achromatic mode has the advantage that the final spot size is
kept small even when the momentum acceptance is large. In monoenergetic mode theenergy loss of the fragments at F4 is independent from their horizontal position at F2.
This mode is employed when a well defined energy bunch is needed at the final focal
plane. For instance, when one is interested in stopping the selected fragments in a thinlayer of matter at the exit of the FRS for β decay measurements. In order to complete

3.1 PreSPEC-AGATA setup in GSI

30

the identification, a system of ionization chambers is used to evaluate the Z value of theions.

Figure 3.2: FRS setup [62]The A/Q ratio is obtained by:
A
eBρ
=
Q
m0 cβγ(3.1)

Magnetic rigidity and time of flight have to be evaluated for each ion on an event by
event basis for the identification. The first quantity is extrapolated by measuring theposition of the ions at the dispersive focal plane (F2) and at the final focal plane (F4).
As regarding Time of Flight, all the beam line in FRS is 70 m long, but in order to havea precise evaluation of beta value of ions, the Time Of Flight is measured between S2and S4 stage. The magnetic rigidity of an ion can be determined from the horizontal
dispersion at the dispersive focal plane (D2 ), the horizontal dispersion at the last focal
plane (D4 ) and the horizontal magnification value between these two focal planes (M4 ).
The two relations [65]:x2 Bρ2 = (Bρ0 )2 1 +
D2

(3.2)


x 4 − M4 · x 2 
Bρ4 = (Bρ0 )4 1 +
D4

(3.3)

show the dependences of the magnetic rigidities in the two stage, S2 and S4. The (Bρ0 )2and (Bρ0 )4 values are associated to ions that cross the focal plane in the central position,
the measurement of the position of every single ion from the centre of the focal planeallows to determine the magnetic rigidity.

Chapter 3: Experimental Setup

31

Timing detectors
The Time of Flight measurement is performed between S2 and S4 stage with plastic scintillator detectors.Two plastic scintillators are placed in S2: standard scintillator (labeledSC21) and a segmented scintillator, called ”FINGER” detector [61]. In S4 stage just one
standard scintillator is used. In order to have the best timing performance and limit
the data throughput just to events where the scintillator signal from both the stage arepresent, the SCI41 signal is used as start while SC21 is delayed and used as stop. The
dimensions of the scintillator SCI21 are 210x80 mm2 , whereas those of the scintillator
SCI41 are 200x80 mm2 . The plastic material BC-4200 (Bicron corp.) provides a high light
output and a fast rise time (∼500 ps). The intrinsic ToF resolution with this system is in
the range of 250 ps.The read-out is obtained with two PMT placed on the left and theright side coupled with fast single hit and multi-hit CFDs. The signal of the two PMTs isdependant from the position of the ion interaction, in fact it is affected by the time thatlight needs to cross the plastic material and reach the PMT surface. The ToF evaluationis therefore obtained considering the quantity [62]:T =1[(SCI21lef t − SCI41lef t ) + (SCI21right − SCI41right )]
2

(3.4)

The ToF value is obtained by summing a proper offset. The β value is obtained dividing the distance between the two scintillators with the ToF and scaling this ratio withthe speed of light. Finger detector is a plastic segmented scintillator, it can be used for
ToF evaluation, as SCI21. Thanks to the segmentation this detector can be used also as
tracking detector.

Figure 3.3: SCI21 standard scintillator, on the left, and Finger detector (15 strips), on the right [66]

32

3.1 PreSPEC-AGATA setup in GSI

Figure 3.4: On left panel scheme of TPC components [66]. On right panel TPC efficiency at different rates [67]Tracking detectors
Ion tracks can be measured using Time Projection ion Chamber or plastic scintillator
commonly used for Time of Flight. The first type of detector is a drift chamber with ahighly uniform electric field. The detector consists of a cathode, where the high voltage
is applied, four anodes and two delay lines. The y-position is deduced from measuring
the drift time of the electrons. As regarding x-position, the signals of the anodes are
splitted and the time difference between left and right side’s signal is compared. This
setup of the detector provides two indipendent x-position measurements and four yposition measurements. The presence of precise delay lines allows to get an accurate
position determination (0.18 mm of spatial resolution on x axes and 0.08 mm on y axes).
The limit of these detectors is the loss in efficiency as the rate increases (Fig. 3.4). As
discussed in previous paragraph, plastic scintillator detectors are used in S2 and S4 forTime of Flight measuerements but they can be used also for position determination.
Standard scintillator read-out is obtained with two PMT placed on left and right side
coupled with CFDs. As a consequence the difference between the two PMT time signals
can be used to evaluate the relative position of the interaction points of the ions insidethe detector. The FINGER detector is a plastic segmented scintillator (15 strips in 2012setup, 70 strips in 2014 setup). Every strip has one own read out with PMT. This is used
for the timing determination but also for measuring the height of the pulse. Knowing
the position of every strip, it is possible to deduce the position of the ion interaction
according to which strip has the most intense signal.

Chapter 3: Experimental Setup

33

Z value evaluation detector
Nuclear charge Z value is estimated with ionization chamber detectors. Two detectors
are operating at S4 stage called MUSICs (Multi Sampling Ionization Chamber). They are
fast multiple sampling detector, with eight independent anode strips, a Frisch grid anda cathode. CF4 is used as counting gas at atmospheric pressure (1013 mbar). Z value
estimation is obtained exploiting the relation:−dE= Z 2 f (β)
dx

(3.5)

In this way, after a proper calibration of MUSIC signals according to the β value, it ispossible to extrapolate the Z value. The indipendent strips allow to obtain a multiple
evaluation of the ∆E and therefore a precise measurment of the nuclei charge.
Y
1/8
δEi
∆E =
∼ Z2

(3.6)

Figure 3.5: MUSIC detector scheme

3.1.2

The calorimeter (ToF and E-∆E) LYCCA

Typical gamma spectroscopy experiments with relativistic exotic ion beams require anhigh precise detection of the outcoming projectiles from the secondary target. The bestsolution is an analysis magnet; if an high resolution magnetic device is not available, anarray of E-∆E telescopes is a good solution for selection of events related to reactionsof interest. The LYCCA calorimeter [59] is a complex system of many particle detectors
designed and realized to fit this aim. It is a flexible array of detector modules for tracking
and characterizing products of reactions on secondary target. It is placed at the exit of
FRS beam line, just some meters after the S4 stage of measurement. It is composed byan array of E-∆E telescopes, a system of Double Sided Silicon Strip Detector (DSSSD)
for tracking ions and a system of large area plastic scintillation detectors for high precise
ToF measurements. In Fig. 3.6 the schematic layout of the array is represented.

3.1 PreSPEC-AGATA setup in GSI

34

Figure 3.6: Lycca array schematic setup [59]

DSSSD detectors for ion tracking
Double Sided Silicon Strip Detectors(DSSSD)are used to track the beam ions before andafter the secondary target. As shown in Fig. 3.6 a DSSSD panel is placed in front of thetarget, while a system of twelve panels are placed far behind the target( at a distance of∼ 3.5 m): these panels form the DSSSD wall that coupled with CsI wall provide E-∆E
wall identification, as shown in Fig. 3.7.
Each tracking module is an ion implanted silicon wafer, silicondioxide(SiO2 ) passivated,and operated totally depleted with floating guard rings. The thickness of these detectors
is nominally 300 - 320 µm and they are squared shaped (60.1 x 60.1 mm2 ) with an active
area of 58.5 x 58.5 mm2 . This area is divided in 32 strips on both front (junction)p-side
and rear (ohmic) n-side in orthogonal directions to provide the position of interaction in
the two dimension. Interstrip distance is 30 µm on p-side while it is 200 µm on n-side.
As regards energy resolution it is 1-2% at 5 MeV (tested with alpha particles) [62].
E-∆E Wall for nuclei identification
The beam line ends in the LYCCA E-∆E telescope array where the residual energy ismeasured with a thick CsI scintillator crystal while the ∆E is measured by a DSSSD

Chapter 3: Experimental Setup

35

Figure 3.7: Technical drawing of Lycca-Wall [62]Figure 3.8: DSSSD panel [59]panel. This array is composed by twelve modules made by a DSSSD panel coupledwith nine CsI detectors (as shown in Fig. 3.9 left panel). The CsI(Tl) crystals originate
from Kharkov, Ukraine [62]. The scintillators front face is 19.0(5) x 19.0(5) mm2 and thethickness is 33 mm (Fig. 3.9 right panel). This array allows to obtain E-∆E matrices
for identification of reaction products (as shown in Fig.3.10). The ∆E energy resolution
allows to have a charge resolution of: ∆Z = 0.55 [59].

Large area platic scintillators for ToF measurements
Large area plastic scintillators are used as start and stop detectors for high precision Timeof Flight measurements. Every scintillator consists of a 2mm thick plastic membrane(type BC-420) with a diameter of 27 cm in a plastic frame, which contains 32 photo multiplier tubes (PMTs). The large number of PMTs allows to improve time resolution because, in principle, every PMT provides an indipendent measurement of the time when
the ion interaction occurs (the reduction factor is ∼ √132 ). Every PMT signal is dependent from the interaction position on the scintillator membrane. Tracking detectors can3.1 PreSPEC-AGATA setup in GSI

36

Figure 3.9: On the left panel E-∆E telescopes module [62]. On the right panel the CsI crystal [62]Figure 3.10: E-∆E matrix from a 63 Co beam run, with a selection on Iron isotopes [59]be used to recover the interaction position with an error of the order of 1 mm per dimension. This allows to correct this position dependent effect improving the time resolutionof the system (expected to be less than 50 ps in the best experimental conditions [62]).
One of these large area scintillators was placed at the exit of FRS (as start) and the otherone was placed in front of the E-∆E Wall (as a stop): in this way it was possible to getan accurate estimation of the projectile ToF and β values on the secondary target. In addition another scintillator detector was placed in front of the secondary target to have aan additional ToF evaluation. The operation way of this detector is the same of the large
area ones but in this case the dimensions are smaller: it has a diameter of 7.3 cm and justnine PMTs on the border.

Chapter 3: Experimental Setup

37

Figure 3.11: picure of 32 Hamamatsu R7400U PMTs mounted on an octagona acrylic glass frame
around a 1 mm thick, 27 cm in diameter BC-420 sheet [68]Using the measurement of ToF it is possible to identify the masses of reaction productswith a resolution of ∆A = 0.55 as shown in Fig.3.12

Figure 3.12: On the left an exemplum of energy vs ToF plot obtained with Lycca. On the rightspectrum of masses obtained with energy and ToF measurement [59]during the first in-beam commissioning experiment in 2010.

3.1.3

AGATA

AGATA is the acronym (Advanced GAmma Tracking Array) for the European project
aimed to construct and develop a new HPGe detector array to investigate nuclear structure by high precision gamma ray spectroscopy. The basic idea consists in exploiting
the good energy resolution, the linearity of HPGe detectors and the possibility of anelectronic segmention of the crystals to build an array able to track the gamma rays incoming on the detectors. The great goal of such apparatus is the possibility to reject3.1 PreSPEC-AGATA setup in GSI

38background radiation not coming from the target without losing efficiency due to thevolume occupied by the anticompton shields and the possibility to have an accurate
doppler correction for gammas emitted in-flight. Even if the geometry is a 4π array,some intermediate phases are planned. In 2009 a campaign started in LNL to test theperformances of a demostrator composed by five triple clusters; the promising resultsbrought to a physical campaign from February 2010 till spring 2012 in LNL. In 2012 thearray was moved to GSI and from autumn 2012 till summer 2014 it was coupled withPreSPEC setup in GSI. In this phase the array was composed by five triple clusters andfive double clusters. Actually the array is operating in GANIL coupled with VAMOS
spectrometer. At the moment of the experiments here discussed, the number of operating crystals was varying between fifteen and twentytwo due to instabilities registeredafter mounting the last produced crystals.

Figure 3.13: Planned AGATA final geometry [39]AGATA geometry and design
The geometry of the array was planned taking in account two different objectives: thefirst was to maximize the efficiency and angular coverage, the second one was an innerspace sufficiently large to host ancillary instrumentation. The best performing geometry was obtained after GEANT4 simulations [38]. The adopted solution consisted in a
sphere composed by 180 hexagons and 12 regular pentagons. Due to the symmetries required for this buckyball structure, the hexagons are grouped in three classes characterized by slightly different shapes (as represented in Fig.3.14). The detectors are grouped
in clusters: 60 triple clusters for the hexagons, each of them contains one crystal per type,while pentagons are canned individually. The detectors of the same cluster are in one
cryostat with a liquid nitrogen system to keep the temperature at 90 o K. Also preampli-

Chapter 3: Experimental Setup

39

Figure 3.14: AGATA triple cluster: the three different hexagonal shapes are labeled with different
colours

fiers require a cooling system to keep them at 130 o K. The inner radius of the array isfixed at 23.5 cm and the photopeak efficiency is expected to be around 50% for 1 MeV
γ−rays [39]. The AGATA Demostrator was characterized by a very compact geometry,as shown in Fig.3.15. The AGATA geometry was changed to suite the GSI setup. In
fact the hole planned in the AGATA array to host the beamline was too narrow for the
beampipe of the GSI laboratory. The solution adopted consisted in a ring composed bytriple clusters coupled to a ring of five double clusters [40] as shown in Fig.3.16.

Figure 3.15: Picture of AGATA Demonstrator in LNL [39]

3.1 PreSPEC-AGATA setup in GSI

40

Figure 3.16: Schematic representation of solution for AGATA geometry in GSI [40]AGATA electronics and Pulse Shape Analysis
The tracking of gamma rays requires high resolution in the determination of the interaction positions: approximately 5 mm of accuracy. This precision cannot be reached using
only electronic segmentation because this would imply a granularity of 30000 voxels per
crystal. This segmentation is too high to be handled, the critical point was solved using a lower segmentation (36 segments per crystal) and applying a pulse-shape analysis
technique (PSA). AGATA detectors are n-type Germanium crystals produced by CANBERRA. They are characterized by semi-coaxial geometry (Fig.3.17) and a segmentationof the outer detector contact in 36 parts. The length is 90 mm, the diameter is 80 mm atrear with a tapering to an irregular hexagonal shape with an angle of 10o at the front.
The sector-wide segmentation crosses the middle of each hexagonal side, while the longitudinal segmentation forms rings with varying thickness: in particular the frontal segments are thinner than the backside ones. This choice has the aim to have a uniform
number of interaction points per segments. AGATA was developed for γ spectroscopy
in an energy range below 4 MeV: the number of interaction points in the first centimeters
is very high. In order to reduce the interactions number per segment, the thickness ofthe frontal segments is shorter than 1 cm. The packing of these detectors was realizedusing the same technology developed for the clusters of EUROBALL array.
The Pulse Shape Analysis requires a digitalization of the signal before the processing of
the data. For this reason all the 37 signals coming from a crystal (36 from the segments
and 1 from the central core electrode) are digitised at 100 MHz after the preamplifier byhigh-resolution (14 bits) fast ADCs. Energy, position and time for every γ-ray interaction

Chapter 3: Experimental Setup

41

Figure 3.17: Schematic representation of AGATA crystal segmentation

can be extracted using the PSA. These data are associated with both a unique time-stamp
and a unique positional label, that are used by the acquisition system to associate signals
from the same event. One of the advantages of digitalization consists in the possibilityof using algorithms like, for example, the Moving Window Deconvolution algorithm tofilter the signal and reconstruct the original charge collected, removing the effect of thepreamplifier. A good energy resolution was achieved using short shaping time: this allows to sustain higher count rates compared to standard HPGe detectors (50 kHz per
detector instead of 10 kHz). The determination of the position of interactions inside asegment with a precision of 5 mm has to face the problem that more than one interaction can occur inside the segment. Important information can be extracted not only bysegments with a net charge deposition but also by the neighbour segments where just atransient signal is registered. The position of the interaction is deduced by comparing
the signals with a reference basis of signals, where each signal corresponds to a well localised single interaction. Thanks to the fact that the detector response is linear, we canconsider the signal from a segment as the superposition, weigthened on the energy, ofthe signals of every single interaction that took place in the voxel:
S(E, t) =N
X

Ei S(xi , yi , zi , t)

(3.7)

i=1

where N is the number of interaction inside the segment. Many approaches have been
proposed to solve this equation: the solution in fact provides the information requiredfor γ-ray tracking. Adaptive grid search [41], neural networks, matrix inversion [42], genetic algorithms [43], recursive subtraction [44] are some of these approaches: actuallygrid search algorithm is the solution applied, thanks to the small processing time thatallows to use it also in on-line acquisition. At the moment the algorithm works on theassumption that the size of the segments is small enough to neglect a multiple interaction

3.1 PreSPEC-AGATA setup in GSI

42

in the segment (this means N=1 in Eq. 3.7). In principle this is not a realistic assumption
but it was shown that this does not affect significantly the real performaces of the apparatus: especially in case of coulomb excitation and fusion reaction experiments. The key
point for PSA is the choice of the signal basis. Experimental signal basis are not available
yet, because they require long time to have sufficient statitistics. At the moment the basis
are obtained with accurate calculations of the charge transported in the detector [45].
Gamma tracking algorithm
The information about the γ-ray interaction points is used in tracking algorithms to disentangle different γ-rays entering in the array and to discriminate and suppress the background. Algorithms avaible for γ-ray tracking can be divided in two classes: algorithms
based on back tracking [46] and the ones based on clustering and forward tracking [47].
The back tracking algorithm exploits the fact that the photoelectric energy deposition ispeaked around 100-250 keV and it is almost indipendent from the energy of the incident
γ -ray. The algorithm assumes that the points of interaction where the energy released isin the range of photoelectric absorption, are the last interaction of fully absorbed γ rays.
From these points the algorithm back tracks the gammas, computing scattering angles
on the basis of the energy released in the interaction. In this way the algorithm can reconstruct the previous intercation and in the end it is able to reconstruct all the γ-ray tracks.
This algorithm showed less efficiency and a worse Peak to Total ratio than the algorithmsof the other class [48]; for this reason it is not actually implemented in the analysis codeused for the experiments discussed here. The forward tracking algorithms start from theidentification of clusters of interaction that could belong to a single γ-ray. In this case
the Compton cross-section abundance in forward direction is exploited. The clusters arecomposed by interaction points with an angular distance between each other (link algorithm) or respect to a given point (leader algorithm) lower than a threshold value. The
next step of this type of algorithms is the investigation of every cluster to determine if
it is composed by interaction points belonging to one single γ-ray. The criteria used forthis evaluation are listed below.
• The tracking algorithm uses the angle-energy relation in Compton scattering toevaluate the most likely sequence of interactions. This is applied evaluating thefollowing figure of merit function:
F oM =

N
−1
X
j=1

Wj

Eγ 0 − Eγpos
0
Eγ

!2
(3.8)

Chapter 3: Experimental Setup

43

where Eγ is the sum energy of the N-1 interactions, Eγpos
is the energy of scattered0photons according to Compton scattering relation. For a cluster of N interactions,
all the N! combinations are tested and the cluster is accepted if for at least one
combination the FoM value is smaller than a predetermined value.
• When a cluster is composed by a single interaction, the algorithm evaluates theconsistency between the energy of the hypothetical γ-ray and the depth reachedin the crystal. If this two quantities are consistent, the algorithm decides if considering it as a photoelectric event or discarding it as spurious Compton scattering
event, using a Monte Carlo approach. If two gammas with 511 keV energy are
identified and an energy release is identified in the middle, the code consider thisevent a pair production and sums the energies.
• The algorithm tries to recover intially descarded clusters, combining them andevaluating the FoM value again. If the obtained value is acceptable, the cluster
is recognised as a good event. If this is not the case, the cluster is definitively
descarded as an incomplete scattering of the incident gammas. In this way it ispossible to obtain a Compton backround suppression, without loosing angular covarage or efficiency due to compton shields. This means an higher photopeak
efficiency and a better Peak to Total (P/T) ratio. Fig. 3.18 shows an example ofclusterization of interaction points in an ideal 4π HPGe shell.
At the moment two forward tracking algorithm are avaible in Narval DAQ system (seesubsection 3.1.5) for experimental data analysis: Orsay ForwardTracking (OFT) [48] andMars Gamma-ray Tracking (MGT) [49]. The last one version is the most used in analysis
codes, and also in the analysis here presented, because it has shown, till now, the best
performances.
AGATA performances
The experimental campaign of the AGATA demonstrator at LNL has provided important information on the performances of the AGATA array. Here a brief summarize of theperformances at high energies will be presented. The aim of the experiments discussed
in this thesis is indeed measuring high energy gamma rays. At LNL precise calibration
measurements provided informations on the energy resolution in the range of 2 - 9 MeV.
Am-Be-Ni and Am -Be-Fe sources were used to cover this wide energy range. This typeof sources exploits the α decay of 241 Am to induce the reaction 9 Be(α,n)12 C. The neutrons emitted are thermalized by a paraffin shield and are used to induce (n,γ) capture

44

3.1 PreSPEC-AGATA setup in GSI

Figure 3.18: Schematic representation of interactions of 30 γ-rays detected in an ideal HPGe 4π
shell, the interaction circled with red line are cluster of interaction correctly tracked, while theones circled with green line represent clusters badly tracked [39]reactions on Fe and Ni (for more details see [50], [51]). In the left panel of Fig.3.19 theenergy resolution is plotted as a function of the energy. Both data for single crystals andall the demonstrator are plotted. It is possible to notice that the data follow the expected√1 trend. Performances at high γ-ray energies were investigated with the measurementEof 15.1 MeV γ-rays emitted in the reaction d(11 B,nγ)12 C at Ebeam =19.1 MeV (for moredetails see [50], [51]). In the right panel of Fig.3.19 the deviation of the centroid of peaks
measured from the tabulated energies is reported: the data from sources and from thereaction described above allow to show that the array is characterized by a very high linearity also at high energies. Another important aspect is the efficiency: in particular theefficiency of tracking algorithms compared to a simple add-back of the energies of interactions identified by PSA. This estimation is strongly dependent from the backgroundand multiplicity of the γ-rays. An overall indication ( [50], [51]) is that tracking algorithms (MGT libraries in particular) have very high efficiency at low energies (below 4
MeV), while at very high energies (above 10 MeV) the performances of these algorithms
decrease: if the background level is sufficiently low the add-back technique can gain 25%
of statistics compared to tracking algorithms. This estimation, as already explained, isstrongly dependent on environmental conditions, for this reason an evaluation valid forChapter 3: Experimental Setup

45

Figure 3.19: Left panel: Energy resolution plotted as a function of γ-ray energy. Data are collectedwith Am-Be-Fe and Am-Be-Ni calibration sources. Empty circles represent data of single crystals,
empty triangles data of add-back of all AGATA [50]. Right panel: Deviation from the tabulated
values of centroid of measured photopeaks, the deviations are expressed as fractions of the energy
measured [51].

all the laboratories in which AGATA array will be uesd, is at the moment not yet fixed.

3.1.4

HECTOR+

HECTOR+ is an array of LaBr3 :Ce and BaF2 scintillator detectors of large volume. The
size of a crystal is 3.5”x8” for LaBr3 :Ce detectors and 7” x 7” for BaF2 detectors.
LaBr3 :Ce detectors have optimal performances compared to other scintillators. They arein particular characterized by an excellent energy resolution (<3% at 662 keV), good time
resolution (<1 ns) and good efficiency.
BaF2 scintillators are carachterized by good efficiency, excellent time resolution (<200ps) but poor energy resolution(∼10% at 1 MeV). The fast decay time 16 ns for LaBr3 :Ceand 0.7 ns for the fast component and 0.7 µs for the slow component of BaF2 allow thesedetectors to stand very high rates.
One aspect to take into accont using LaBr detectors is the internal radiation. These crystals contain 138 La that have a mean life of 1011 y and a contamination of 227 Ac [71]. The
decay of these radioactive nuclei and the one of their daughter nuclei produce the wellknown spectrum of internal radioactivity shown in Fig. 3.20. This scintillators arrayis characterized by large volume detectors to increase efficiency in order to detect highenergy γ rays. In the 2012 setup ten LaBr3 :Ce detectors were used coupled with eigth
BaF2 detector, while in the 2014 only two LaBr3 :Ce detectors were missing as installed in3.1 PreSPEC-AGATA setup in GSI

46

Figure 3.20: Energy spectrum of the internal radioactivity of a LaBr detector [71].

LaBr
142

o

BaF

2012

2014

2012

2014

2

0

4

4

o

98

4

2

4

4

o

68

4

4

0

0

22o

0

2

0

0

Table 3.1: number of scintillator detectors at different angular positions in 2012 and 2014 setup.

Riken laboratory. These detectors were placed at different angles as shown in Fig. 3.21.
LaBr3 :Ce scintillators were placed at forward angles. Their performances at highenergy were tested and simulated [58] showing high efficiency and a good energy resolution, as shown in Fig. 3.22.

Chapter 3: Experimental Setup

47

Figure 3.21: HECTOR+ setup in 2014, red detectors are LaBr3 :Ce scintillators while the light green
ones are BaF2 scintillators, in grey the AGATA clusters

3.1.5

The Data AcQuisition system at GSI

The main features of the complex data acquistion system used in GSI for the experiments
discussed in this PhD thesis, are here described. These informations are based on [57]
where more details can be found.
GSI DAQ for PreSPEC AGATA setup was built using two main actors: GSI DAQ system MBS [69] and GTS-NARVAL [70] DAQ system. The former was reposnible for thetriggering logic and data collection from FRS, LYCCA and HECTOR+ systems while thelatter was dedicated to AGATA. The complexity of the acquisition is mainly connnectedwith the different nature of the systems: analogue system for MBS side and completely
digital for GTS(Global Trigger and Synchronization system)-NARVAL side.
The MBS DAQ is organized in eleven branches, each branch is equipped with: a VME
crate controlled by a RIO3 or RIO4 processor, a TRIVA trigger module. The TRIVA modules are linked together to guarantee that the system operates synchronously. This DAQ

48

3.1 PreSPEC-AGATA setup in GSI

Figure 3.22: On left panel: gamma spectrum of the reaction 11B (p, γ)12C at 17.6 MeV acquiredwith LaBr3 :Ce scintillators. It is possible to see a clear separation of full energy peak and single
escape [58]. On right panel LaBr3 :Ce scintillator efficiency obtained with GEANT3 simulations[58].

system is divided in three subsystems: one for FRS, one for LYCCA and one for HECTOR+. Each subsistem has a proper MH-TDC: this module allows to record the time of
all hits. In this way it is possible to monitor and check the hits time distribution. It is
possible therefore to monitor the presence of a ”good” hit, using an external time reference coming from the scintillator of the last focal plane in FRS.
In this setup the Master crate was labelled TRLO (TRigger LOgic). It assured the synchronous read out of all crates for every Master trigger generated by a TRLO firmware.
TRLO crate included also an AGata VME Adaptateur (AGAVA) that allows to couple
VME-based system to AGATA system and GTS timestamp for any MBS event.
As previously explained, the signals from AGATA detectors are processed by digitizers.
They run with a common clock provided by GTS. The GTS also gurantees the timestamping. Data are stored till trigger processor decides for validation or rejection. In case of
rejection the event is descarded, in case of validation it is sent to computer farm.
The GTS, the AGATA triggering system, is organized as a tree where the leaf are the crystals, as shown in Fig. 3.23. When a core crosses the threshold a request is sent to trigger
processor. The decision of the processor is sent back to the requesting module throughthe tree. The configuration of this system foresees two partitions: one for AGATA detectors, one for particle and ancillary detectors. When a partition asks for a trigger, it is”up” for 1 µs. A coincidence is set if both of them are up for 6µs, with a coincidence window ±3 µs around the ancillary request. Each GTS leaf that has a request in coincidence
window is validated. The full system is validated by VME based electronics. The trigger

Chapter 3: Experimental Setup

49

Figure 3.23: GTS organization scheme. Every detector is a leaf, when the core signal rise up fromthe threshold a request is submitted to trigger processor (blue arrows). GTS AGAVA represent all
the other detectors in PreSPEC setup, therefore for every MBS event it sends a request to trigger
processor (green arrows). It validates the γ-rays event coincidences and sends back the decision(red arrows) [57].

decision inside GTS system takes 10 µs. However in PreSPEC the count rate is so highthat it is not possible to use such type of trigger hierarchy. Therefore the read out of thesystem is controlled by the trigger from TRLO firmware.
NARVAL system foresees for every detector three different ”actors”. Each actor apply an action to the data: the ”producer” collect the signal from the carriers, the ”preprocessing” apply energy calibrations and time allignements, the ”PSA” apply a gridsearch analysis to assign the position coordinates to every interactions. Other three actors operate after these first three. The ”Event Builder” builds the event according totimestamps, the ”Merger” merges PreSPEC and AGATA data, while the ”Tracking” apply tracking algorithms to AGATA data to disentangle the γs.
The time required by MBS to process data is at least 90 µs. The easiest way to reducethe dead-time is to select only good event to be written. Scintillator in last focal plane of
FRS provides the trigger request for the incoming ion from FRS, the plastic scintillator in
front of the secondary target and the plastic scintillator in front of the wall provide thetrigger request for LYCCA: without tracking of the ion no doppler correction is possible
and the data are useless. As regards γ triggers, copies of AGATA detector core preampli-

50

3.1 PreSPEC-AGATA setup in GSI

fier signals are sent to analog CFDs and a logic OR is used for a γ trigger request, a logic
OR of HECTOR+ signals, after a coincidence with plastic scintillator in last focal plane,
is used as further γ trigger request.
The calibration of the detector system, the beam and the gain drift monitoring required
dedicated triggers. Three different triggers were setted to collect in-beam data. One trigger (labelled with number 10) required just one signal in scintillator in last focal plane:
this trigger was properly scaled down and it was used as normalization trigger. It isindeed the most bias free trigger. Another trigger (number 9) required coincidence with
FRS, LYCCA and AGATA, while the last one (number 8) required FRS,LYCCA and HECTOR+. The hierarchy between triggers were defined by the number of the trigger. Inside
MBS event a tag from AGAVA was written in addition to GTS-timestamp. MBS event
was written for both the tags. In this way GTS system did not discard events with γ rays
detected only by HECTOR+. Verifications were performed using an MBS process, theTime Sorter, to prove the consistency between MBS and NARVAL (see Fig. 3.24). This
proof demonstrated the possibility to sort event-by-event the data collected with MBS
and NARVAL.

Figure 3.24: comparison between the core energy spectrum for one crystal of AGATA acquiredwith NARVAL system and MBS system [57].

Chapter 3: Experimental Setup

3.2

51

DALI2-HECTOR+ setup in Riken

One of the experiments here discussed was performed in RIKEN laboratories with DALI2 setup. RIKEN laboratories have created a very important facility for radioactive ion
beams. This facility is called RIBF (Radioactive Ion Beam Facility); it can provide primary beams up to 440 MeV/nucleon (350 MeV/nucleon for heavy ion beams) and thegoal is to reach 1pµA of intensity. These performances are obtained using a variablefrequency-heavy-ion linac (RILAC) as injector in a sequence of four ring cyclotrons. The
cyclotrons: RRC (ring cyclotron),fRC (fixed frequency ring cyclotron), IRC (intermediatering cyclotron) and SRC (superconducting ring cyclotron) deliver the beam in an isotope
separator where a primary target is used to produce the radioactive beams. This separator is called Big RIPS and it allows to produce and select exotic ion beams. In the
DALI-2 setup, the isotope beam of interest is delivered on a secoondary target where thereactions under investigation take place. This target is rounded by an array of NaI scintillator γ-ray detectors (DALI2). These detectors allow to study γ ray emission inducedby the reactions on the target. The reaction products coming out from the secondary target are identified with a magnetic spectrometer: ZDS (Zero Degree Spectrometer). Herea brief description of the setup will be presented, using [55] and [5] as main references.

Figure 3.25: Scheme of the RIBF facility at RIKEN

3.2.1

Big Radioactive IsotoPe Separator

BigRIPS is a magnetic separator used to produce and select Rare Isotopes Beams. The
main characteristics of this separator consist on the large ion-optical acceptance, the two

52

3.2 DALI2-HECTOR+ setup in Riken

stage structure and the high precision particle identification. The advantage of a large acceptance mode of operation consists in the possibility to use 238 U fission reaction mechanism, beside the usual fragmentation reaction. This allows to enlarge the neutron rich exotic area accessible with the beams. The first stage of BigRIPS is dedicated to production
and separation of rare isotope beams, while the second one is used for analysis and identification of the beams provided. The beamline of BigRIPS is 78.2 m long: two dipoles
and four superconducting tiplet quadrupoles are placed in the fisrt stage while ten superconducting tiplet quadrupoles and four dipoles are present in the second stage. The
dipoles are operating at room temperature and the bending angle is 30 degrees. Except
the two triplets at the border between the two stages, every tripet quadrupole (STQ) isequipped with a superconducting sextupole to correct second order chromatic and geometrical aberrations. The large acceptance is determined by large aperture quadrupoles:± 40 mrad of angular acceptance horizontally and ± 50 mrad vertically with a momentum acceptance of ±3%. The two stages are designed as a mirror-symmetric achromatic
system: achromatic conditions are fullfilled at the three focal planes on the beamline (denoted with F2, F3, F7). The separation of the fragments is achieved by magnetic rigidity
analysis and the energy loss in achromatic degraders with wedge shapes inserted at dispersive focal planes (namely denoted with F1 and F5).
As introduced before, while the first stage is used for production and separation of RI
beams, the second one is focused on the analysis of the beam. The identification is obtained with the same technique used in FRS: Time of Flight and positions at focal planes
are measured to estimate the A/Q value of the ions, while a ionization chamber is used
to evaluate the charge of the ions, that corresponds to Z value, except in the case of
charge states.

Figure 3.26: Scheme of the BigRIPS setupChapter 3: Experimental Setup

53

Time of Flight measurement
Time of Flight is obtained with two platic scintillators placed along the beam line at F3
and F7 focal plane (Fig. 3.27). The dimension of the active area is: 120mm x 100mm. The
timing resolution is lower than 100 ps, but the performances of these detectors are affetcted by radiation damage: for this reason every 48 hours of beamtime the scintillators
has to be changed.

Figure 3.27: Picture of one of the two scintillator used for F3-F7 Time of Flight

Position measurement at focal plane
Every focal plane is equipped with position-sensitive parallel plate avalanche counters(PPAC) in order to estimate the position of the ions. These detectors provide a twodimensional measurement of the position of the ions. As shown in Fig. 3.28 on bothdimensions the signal produced by the incoming particle is splitted and sent to tworead-outs through a delay line. The estimation of the time differences of the read-outs
can be used to extrapolate the interaction position. Position resolution is depending fromthe charge of the ions incoming. For Nickel isotopes it is expected to be 0.2-0.3 mm. Thiskind of detectors are affected by electrical discharge, the usage of Ag electrodes reduces
this phenomena. Another chritical aspect is the rate acceptables for this detectors: for Z
values of the order of ten the maximum rate is 1 Mcps.

Charge measurement
As in FRS the charge of the ions is measured with a MUlti-Sampling Ionization Chamber (MUSIC). As shown in Fig. 3.29 6 channels for read-out are used. The resolution
obtained is ∆Z=0.21 . This value get worse when the count rate increase: in particulararound 100 kpcs the recombination of electrons and ions worsens the resolution.

3.2 DALI2-HECTOR+ setup in Riken

54

Figure 3.28: Scheme of the operating mode of PPACs [52]Figure 3.29: Scheme of the MUSIC used in BigRIPS [52]3.2.2

Zero Degree Spectrometer

The Zero Degree Spectrometer is a magnetic spectrometer to analyze reaction products
in experimental setups where the RI beam is delivered on a secondary target placed at
the stage labelled as F8. It consists in a two-bend achromatic system with anti-mirror
symmetry. It is composed by two dipoles and six triplet quadrupoles with the same design of the ones used on BigRIPS beamline. The final focus stage (F11) is fully achromaticin the standard operating way of ZDS. The transport from F7 to F8 is achieved using two
triplet quadrupoles as dispersive telescope to match BigRIPS setup with Zero Degree
Spectrometer setting.
If the radioactive beam is delivered at F11 stage, the ZDS is tuned to maximize the transmission efficiency.
ZDS can be used in different operating ways, for example it can be used in achromatic
large acceptance way or in high resolution dispersive setup. The mode is chosen de-Chapter 3: Experimental Setup

55

Figure 3.30: Technical drawning of Zero Degree Spectrometer

pending on the experiment requirements. During the experiment here discussed theZDS was setted with large acceptance setting.
The identification method is the same used for BigRIPS, and also the detector types involved. On F11 a Total Kinetic Energy counter is used: it is a LaBr3 :Ce detector 3”x3”
in which the ions are implanted. The aim is refinining the identification, to identify andexclude charge states.

Figure 3.31: Picture of the TKE counter at F11 [53]3.2.3

DALI2 and HECTOR+

The experiment about coulomb excitation of 70 Ni was performed with a particular setup:
the array DALI2 coupled with eight large volume LaBr3 :Ce detectors (HECTOR+). DALI2
is an array composed by 186 NaI(Tl) scintillators for γ detection. It is an evolution of aprevious array: DALI (Detector Array for Low Intensity radiation) realized in RIKEN
for the old facility which provided only light exotic beams at v/c ∼ 0.3. It consisted of 64
NaI(Tl) crystals 6 x 6 x 12 cm3 surrounding the target and two sets of plastic scintillators,
one placed at the top and the other at the bottom of the array. NaI(T) detectors wereused to investigate γ-rays emitted by the target while the plastic scintillators were used56

3.2 DALI2-HECTOR+ setup in Riken

to avoid cosmic background [54]. Three types of NaI(Tl) detectors compose DALI2: 45 x
80 x 160 mm3 and 40 x 80 x 160 mm3 parallelepiped crystals were produced by SAINTGOBAIN and SCIONIX while the other type (60 x 60 x 120 mm3 ) was produced by BICRON. HAMAMATSU PMTs (model no R580) are coupled to these crystals, the former
two types use 38 mm diameter PMTs while the last one 50 mm. Alluminium housing 1
mm thick is used for all the detectors, in addition the PMTs are surrounded by µ-metal.
Fig. 3.32 shows the geometry of the DALI2 array. The detectors are placed on 12 layers,

Figure 3.32: Schematic picture of DALI2 geaometry [5]each of them holds up 6-14 detectors. The distance from the target and the positionsof the crystals change layer by layer. The minimum distance from the target is 30 cm,
corrisponding to detectors at 90o , while the angular width of single crystals is around 6o ,(estimated for detectors at 60o ). Fig.3.33 shows the detectors position on different layers.
The aim is to increase efficiency, taking into account the doppler boost for the typicalbeam velocity delivered by the facility (β ∼ 0.6). The choice of NaI(Tl) detectors was
the result of a compromise between intrinsic energy resolution, detection efficiency andcosts. These detectors can provide 9% of energy resolution at 662 keV (137 Cs standard
source). As regarding the electronics, the signal is shaped with 3 µs of time costant before being delivered to a peak-sensing analog-to-digital converter (CAEN V785 ADC).
Time information is obtained by a time-to-digital converter (CAEN V1190 TDC) after ashaping of the signal with 100 ns of time costant and the processing made by a CFD.
The large dimension of the array allows to cover an angular range from 15o to 160o : thismeans an angular coverage of almost 90%. This aspect is relevant for determination of
the multipolarity of the radiation emitted from the target, this wide angular range allows
to fix the angular momentum that characterizes the γ-rays detected. Fig. 3.34 shows thecontributions to the energy resolution in the centre of mass frame at different angles, inChapter 3: Experimental Setup

57

Figure 3.33: Top panel: geometry of 10th and 11th layers. Bottom panel: geometry of last layer(forward angles) [5]the case of 1 MeV γ-rays emitted in flight at v/c of 0.6. It possible to see that the energy
resolution remains around 10%. The performance for efficiency in this experimental condition is expected around 20% for 1 MeV γ-ray. The high granularity of this array allow
to implement algorithms to increase efficiency and peak to total ratio. In particular addback analysis is based on the hypotesis that the signals from neighbouring detectors are
due to Compton scattering of one γ-ray. This means that summing these energies allows
to reconstruct the energy of the incoming γ-ray. The angle for doppler correction is obtained by the angle of the detector with the highest energy release, because it is assumed
to be the first one in which the γ ray interacts. This clustering algorithm allows to suppress Compton background, the key point is the estimation that the events in which two
different γs interact in the same detectors cluster are fewer than the 20% of the all statistics. On the other hand, the operation of energy summing requires careful consideration
related to the nonlinear response of the detectors. In the experiment discussed in thisthesis DALI2 was coupled with LaBr detectors of HECTOR+ array (described in 3.1.4).
The organization in layers of DALI2 allows great flexibility: the forward layer was dismounted and it was replaced with a layer holding the eight LaBr detectors as shown in
Fig. 3.35. The detectors were oriented at 30o with a distance from the target of ∼ 34 cm.

3.2 DALI2-HECTOR+ setup in Riken

58

Figure 3.34: Expected energy resolution for 1 MeV γ-ray in center of mass frame at different angles(in laboratory). Here a β=0.6 is considered and the distance from the target is the nominal one
of DALI (at least 30 cm). The diagram represents also all the contributions. Dashed curve, theintrinsic resolution; dotted curve, the finite opening angle of detectors; dash-dotted curve thespread in velocity of the source [5]An additional LaBr detector (3” x 6”) from RIKEN laboratories, was placed at 90o .
3.2.4

The Data AcQuisition system

The RIBF Data AcQuisition is a distributed network system, based on the idea that themodularity of the DAQ reflects the interchangeability of the detector apparata in different setups. In fact, except for Big-RIPS, all the other detector systems can change fromone experiment to the other. As shown in Fig.3.36, the DAQ is divided in blocks: every
detector system has its own block and it can work as if it were in a stand-alone system. Every block has its own Event Builder, called Slave Event Builder. The system isequipped with CAMAC and VME data modules connected in parallel to the front-end
computers. The data processing is ruled by a software package called ”babirl DAQ”:
the Master Event builder receives data from the Slave Event Builders and constructs thewhole event data. This arrangement of the DAQ system allows to reduce the dead time
under 100 µs. The data are stored on a RAID system and are written in RIBF Data Format(RIDF). During the experiment here discussed, the master trigger required a coincidenceof F7 plastic scintillator with F11 plastic scintillator and with a logic OR between: LaBr
and DALI detectors. Three different triggers were used in the data analysis: F7 plastic

Chapter 3: Experimental Setup

59

Figure 3.35: Diagram of the geometry of DALI2 coupled with LaBr detectors (HECTOR+

Figure 3.36: Scheme of RIBF DAQ. The boxes represents computers [56]scintillator in stand alone mode (properly scaled down), F7 and F11 scintillators in coincidence with DALI and F7 and F11 scintillators in coincidence with HECTOR+. The
time required for DAQ start was 1.2 µs and the acquisition was closed ∼500 ns after.
During this experiment new modules for analysis and conversion of the signal of LaBr
were used. These modules, called QTC (Charge to Time Converter), are based on the observation that there is a relation between the height of the electric pulse and the width.
These modules exploit the leading and trailing edge time of the signal to reconstruct theenergy release. The timing information is provided by TDC V1190 modules. Even if in
the present data analysis their informations were not used, they showed good perfor-

60

3.2 DALI2-HECTOR+ setup in Riken

mances and they will be used also in future experiments.

C HAPTER 4

Data Analysis

The aim of this thesis is the investigation through Coulomb excitation of rare isotope
nuclei. As shown in the previous chapter this has required a complex experimental
setup for producing, identifying and selecting ions of interest and their reactions. An
accurate data analysis needed to be developed in order to select ”good” events andproduce gamma ray spectra from the signals of the different detectors. In this chapter
the processing and the conditions applied to the data is described for data from boththe laboratories (GSI and RIKEN). In particular, the procedure to identify the ions ofinterest, the selection of coulomb excitation events and the gates and conditions applied
to reduce background in gamma ray energy spectra will be explained. In conclusion ofthis chapter the final gated gamma ray energy spectra will be shown.

4.1

PreSPEC-AGATA data analysis: Identification and selection of the
ions

4.1.1

Calibration of the detectors for identification

As explained in the previous chapter, identification of the ions incoming on the secondary target is performed with the FRS system. A lot of detectors are needed: TPCs,
scintillators, ionization chambers. The signal of every detector has to be calibrated andtuned to have the correct identification.
As regarding A/Q estimation, both positions at focal planes and Time of Flight areneeded. TPCs can provide high resolution position information, while the scintillators
are characterized by a lower resolution.
TPCs signal can be calibrated using a fiber mask as position and spacing of the mask are
known, it is possible to obtain a precise calibration (Fig. 4.1 shows an example).
61

62

4.1 PreSPEC-AGATA data analysis: Identification and selection of the ions

The scintillator position signal can be calibrated using TPCs as reference.
Time of Flight calibration requires the primary beam: knowing the thickness of all the

Figure 4.1: In the panel exemplum of the pattern used to calibrate TPCs positionmaterials on the beam line, it is possible, using the LISE calculator [72], to calculate theexpected ToF and to compare it with the signal processed with TACs and TDCs.
A correct estimation of the ToF and therefore of the β value is very important for theMUSIC chambers. In fact, as shown previously, the estimation of the charge of the ionsis dependant from both the ∆E measured by the ionization chamber, and from the velocity of the beam.

4.1.2

Commissioning with isomers

A commisioning run was focused to check that the FRS setup and the particle identification correctly worked. A 66 Cu ion beam was produced, selected and implanted in aplastic degrader at the seconary target stage.
This ion is produced in one isomeric state at E*=1154 keV with an half-life of 600 ns.
Time of flight of ions to complete all the FRS beam line is of the order of some hundredsof nanoseconds: this means that most of the ions in the isomeric state decays after the
implantation (Fig. 4.2 shows the scheme of the decay).
It is possible to select ions with FRS identification and using the AGATA array to checkthat the gamma ray spectrum shows the decay of this state.
The Z vs A/Q matrix (the FRS identification plot) obtained with FRS (Fig. 4.3) permits
to clearly identify the incoming ions. The left panel of Fig. 4.4 represents the gamma ray
spectrum obtained gating on 66 Cu ions while the right panel of the same figure shows

Chapter 4: Data Analysis

63

Figure 4.2: Gamma decay of isomer state of66 Cu

Figure 4.3: Identification plot of ions obtained with FRS: AoQ values are on the x-axes and Z
values are on the on y-axes

the gamma ray spectrum related to 65 Cu (the neighbour bump in the ID matrix). It isclear that the peaks related to the isomer decay appears only selecting 66 Cu.

64

4.1 PreSPEC-AGATA data analysis: Identification and selection of the ionsFigure 4.4: Left panel, gamma ray spectrum obtained gating on 66 Cu: it is possible to see thecharacteristic peaks related to isomeric decay of 66 Cu. The 86 keV transition is not shown because
at this low energy the atomic background in the spectrum is too high. Right panel, gamma ray
spectrum obtained gating on 65 Cu: none of the peaks of 66 Cu are present here (the two peaks inthe figure are the 511 keV peak and the γ ray emission due to neutron capture from Ge nuclei inthe detectors), showing the good identification and selection with FRS

4.1.3

Identification performance during Iron beamtime

In 2012 setup we measured 64 F e from the fragmentation of a primary beam of 86 Kr at
730 AMeV on a 4g/cm2 thick 9 Be target with an intensity of 8 · 109 pps.
In 2014 the secondary 62 F e beam was obtained with primary beam of 86 Kr at 700 AMeV
on a 2.5g/cm2 9 Be target and an intensity of 8 · 108 pps.
The setup for 62 F e was affected by instabilities in SIS synchrotron: the intensity and theenergy of the beam were not constant in time, as shown in Fig.4.5. This aspect requireda fine tuning, run by run, for data analysis.
The setup for 64 F e, was characterized by an high intensity secondary beam at S2 stage:

Figure 4.5: The profile of the β value distribution measured with FRS: in blue all the statistics
acquired, in red only statistics related to 62 F eChapter 4: Data Analysis

65

Figure 4.6: On left panel efficiency of TPC with different ions at varying the rate. On right panel, S2
standard scintillator position signal is plotted respect the position obtained with TPC, it is possible
to see that the uncorrelated events are too many to obtain a good calibration(∼ 5 · 105 Hz). This choice was based on the necessity to accumulate as much as possible
statistics, considering that Finger detector can sustain such an high intensity. Howeverhigh count rate affected TPC efficiency and standard S2 scintillator resolution.
The TPC efficiency to detect light ions is lower than that for heavy ions, in addition thedetection efficiency decreases with the count rate as shown in the left panel of Fig. 4.6).
The figure shows the performances of TPC for Uranium and Xenon beams comparedwith the efficiency that we got for 62 F e at 105 Hz.
In 2012, for 64 F e, the rate was five time larger than the one for 62 F e. This had as a consequence a decrease of TPC detection efficiency of approximately 60%.
Also standard scintillator performance was affected by the rate. The right panel of Fig.4.6
shows the correlation between the S2 scintillator position signal and the position in
TPCs. In standard experimental conditions this correlation would show a clean diagonal curve without any event outside to allow the calibration of the scintillator position
signal. It is evident that in our case it is not possible to perform any precise calibration.
Another aspect that worsed the performances of the scintillators in the 64 F e setup was
the fact that an high intensity Pb beam was used in the experiment performed just before
the 64 F e one. This beam infact damaged the scintillators materials.
The offline analysis showed that the ”Finger” detector was not operating correctly in2012. It was changed for the measurement in 2014, but the instabilities of the new detector made it not working as expected, also during the 62 F e runs. Therefore, no information from the finger detector was used and it was excluded from the analysis.
These experimental difficulties, reduced significantly the identification efficiency.
Both the measurements of 62,64 Fe were not performed in optimal conditions: in both

66

4.1 PreSPEC-AGATA data analysis: Identification and selection of the ions

2012

2014

Primary beam Intensity∼ 8 · 109 pps∼ 8 · 108 pps

S2 count rate

∼ 5 · 105 Hz∼ 1.2 · 105 Hz

60%

85%

TPC detectors efficiency

Table 4.1: Intensity of the primary beam, count rate at S2 stage and TPC detector system efficiency
in 2012 and 2014 setup.

cases the Finger scintillator could not to be used. In 2012 the TPC detectors were not operating in an optimal way and in 2014 the intensity and the energy of the primary beam
were respectively smaller than expected and fluctuating.

Chapter 4: Data Analysis

4.1.4

67

Identification for Iron beams

The PreSPEC setup is designed to identify the components of the cocktail beam optimized for 64 F e and 62 F e. Figure 4.7 shows Z vs A/Q matrix for 64 F e (top panel) and62

F e (bottom panel). The top panel shows higher background if compared with thematrix in the bottom panel. This is due to lower performances of ToF and ion tracking
detectors described in the section 4.1.1 because of high rate and TPC degrader performances.
Charge states are not expected to be relevant for relativistic beams with low Z value [72],[73]. Through the evaluation of the energy loss in the degrader, an estimation of thecharge state contribution to Iron statistics showed no events from charge states of heavier nuclei as expected.
In conclusion the FRS setting allowed to indentify and select the ions impinging on thesecondary target with an efficiency of 85% for 62 Fe and 60% for 64 Fe (as reported in table
4.1). This selection in the data analysis was obtained with gates on the Z vs A/Q matrix:
the red circles in Fig.4.7 represent the gates applied for the analysis.
The data analysis described in the next sections was performed after applying these gateson the beam incoming on the secondary target.

68

4.1 PreSPEC-AGATA data analysis: Identification and selection of the ionsFigure 4.7: Upper panel: identification plot (A/Q value on x axes and Z value on y axes) obtainedwith FRS for 64 F e with 2012 setup; the red circle represent the gate applied to select the 64 Fe
events. Lower panel: identification plot (A/Q value on x axes and Z value on y axes) obtainedwith FRS for 62 F e with the 2014 setup; the red circle represent the gate applied to select the 62 Fe
events.

Chapter 4: Data Analysis

4.2

69

PreSPEC-AGATA data analysis: identification and selection of reaction products

4.2.1

calibration and identification

LYCCA calorimeter was used to identify and select the reaction products after the interaction of the secondary beam in the secondary target. All striped DSSSD detectors andCsI scintillator detectors were aligned (Fig. 4.8 and Fig. 4.9 ) before the calibration.

Figure 4.8: Exemplum of alignement of a cluster of 9 CsI detectors: on the left panel the raw
aligned spectra for each detector is shown, on the right panel the superposition of all the aligned
spectra are shown. The difference in statistics depends on the position of every detector withrespect to the center of the beam line

The PMT signals for the ToF evaluation were aligned in time and corrected withrespect to the position of interaction. In large scintillator membrane the signal of the PMT
is affected by the time needed by the scintillation photons to travel from the interaction
point of the beam to the PMT surface. It is important to correct this dependence with the
hit position to achieve the best timing resolution (Fig.4.10 ).

70 4.2 PreSPEC-AGATA data analysis: identification and selection of reaction products

offsetslope

PMT 00-519.36

0.008

PMT 01-518.674

0.012

PMT 02-517.64

0.008

PMT 03-518.247

0.01

PMT 04-516.729

0.0076

PMT 05-516.458

0.009

PMT 06-516.217

0.009

PMT 07-515.637

0.007

PMT 08-514.463

0.008

PMT 09-514.422

0.008

PMT 10-515.323

0.008

PMT 11-515.647

0.009

PMT 12-515.426

0.008

PMT 13-515.90.007

PMT 14-517.178

0.0076

PMT 15-519.2

0.009

PMT 16-515.894

0.008

PMT 17-514.988

0.009

PMT 18-514.887

0.007

PMT 19-514.026

0.005

PMT 20-513.975

0.009

PMT 21-513.612

0.0097

PMT 22-512.932

0.006

PMT 23-513.632

0.008

PMT 24-512.309

0.007

PMT 25-512.096

0.007

PMT 26-513.228

0.0116

PMT 27-513.149

0.008

PMT 28-512.821

0.008

PMT 29-513.018

0.004

PMT 30-514.394

0.007

PMT 310

0

Table 4.2: Exemplum of parameters to correct position dependece of PMT time signal

Chapter 4: Data Analysis

71

Figure 4.9: Exemplum of alignement of the strips af a DSSSD panel: on the left panel the raw
aligned spectra for each strip, on the right panel the superposition of all the aligned spectra isshown.The difference in statistics depends on the position of every detector with respect to thebeam line

Figure 4.10: Exemplum of a corrected PMT signal.On y-axes the time corrected and on x-axes the
distance in the plastic scintillator between the interaction point and PMT surface

The alignement and the calibration of the Wall detectors allowed to identify the reaction products with the E-∆E matrix. In particular this allowed to select events in which
the reaction product is the same as the incoming ion. This issue is extremely importantin the data analysis as we needed to select projectiles which were excited and decayedwithout particle emission. Fig. 4.11 shows clearly the quasi-elastic bump, the red circle
shows the gate applied for the selection of the projectile excitation events.

72 4.2 PreSPEC-AGATA data analysis: identification and selection of reaction products

Figure 4.11: ∆E-E matrix: ∆E measured with DSSSD panels in the Wall, and E measured withCsI modules. It is possible to see clearly the quasi-elastic bump, related to events in which theoutcoming ion is the same of incoming.

4.2.2

Test of consistency between FRS and LYCCA frames

The ToF evaluation with LYCCA scintillators is an important observable for a good estimation of the projectiles β values on the target. In fact the doppler correction for in-flightemitted γ rays requires a carefull estimation for both trajectory and velocity of the projectile.
Tests of consistency between FRS and LYCCA evaluation of ToF and ion tracks were performed.
The β value measured in FRS was compared with the β value measured in LYCCA (leftpanel of fig.4.12). As expected the fastest ions in FRS corresponds to the fastest ions in
LYCCA, at least in average. The figure 4.12 shows this relation together with a considerable spread of the two distributions: this is probably due to the thickness of the materials
that the beam has to pass through. Also the consistency in tracking ions is relevant forcoulomb excitation events selection, because this selection is based on the scattering angle estimation. In fact, the scattering angle is related to the minimum impact parameter:
if the minimum impact parameter is sufficiently large the probability of an excitation of
the projectile due to the nuclear interaction with the target can be considered not significant with respect to the coulomb excitation (for more details see 4.2.3).

Chapter 4: Data Analysis

73

Figure 4.12: Left panel: comparison between estimation of the β value obtained with FRS and
LYCCA. The width of the β value distribution in LYCCA is related to the thickness of the targets.
Right panel: comparison between the position detected with DSSSD target and the position on
DSSSD target obtained by TPCs interpolation.

In order to perform the angle evaluation, TPCs in S4 stage were used to estimate thetrajectory of the ions incoming on the target, while DSSSD panels were used to track theions outcoming from the target (Fig. 4.13 shows the patterns of the beam on the DSSSD
target and Wall).
For this reason the position estimation with TPCs and the one obtained with DSSSDs
before the target was compared to check the alignement of the two systems. This test
showed that only a very small discrepancy of a few millimeters between TPCs and
DSSSD. On the basis of this discrepancy it was possible to have an indication of theaccuracy of the evaluation of the scattering angle. We obtained a maximum uncertainity
in the determination of the scattering angle of less than 2 mrad.

Figure 4.13: Left panel shows the beam pattern measured with the target DSSSD; right panel
shows the beam pattern measured with Wall DSSSD.

74 4.2 PreSPEC-AGATA data analysis: identification and selection of reaction products

4.2.3

Coulomb excitation selection

The next step of the data analysis, namely the γ ray spectra investigation (see section4.3), was performed after the selection of scattering angle in order to select Coulomb
excitation events.
The selection of the Coulomb excitation, in the target-projectile collision, is based on
the consideration that if the minimum distance of approach is larger than the nuclear
interaction range, the excitation of the projectile (or the target) occurs via electromagnetic
interaction and not via nuclear interaction.
The minimum approach distance and the minimum impact parameter are connected by
the relation:

b=

D2 −

2aD
γ

 12
(4.1)

where a is:

ZT ZP e2
(4.2)
m0 c2 β 2where m0 is the reduced mass. It is possible to see from relation 4.1 that at relativistica=energies bmin →D, therefore in the next discussion they will be considered the same
quantity.
The minimum distance between the target and the projectile to consider the excitation
as a result of coulomb interaction, is commonly considered the sum of the nuclear radiiof the target and the projectile.
Here, following the approach discussed in [84], this minimum distance is computed
using the following relation:
Cp + Ct
(f m)
(4.3)
6.35
where Cp and Ct are two parameters respectively related to projectile and target nucleus,
Rint = Cp + Ct + 4.49 −that are obtained from:
C = R(1 − 1/R2 )(4.4)

In this relation the projectile radius has to be used for Cp and target radius for Ct . The
nuclear radii are obtained using the relation:
R = 1.28A1/3 − 0.76 + 0.8A−1/3(4.5)

As a result of this discussion, the coulomb excitation selection is based on the selectionof the minimum distance approach. This distance is related to the scattering angle byChapter 4: Data Analysis

75

the relation explained in [83] and here reported:θlab =

2.88 × Zt Zp × [931.5 + Elab ]1
× [rad]2 + 1863 × E
Ap × [Elab
]
D
lab

(4.6)

where Elab is the laboratory beam energy expressed in AMeV. The scattering angle selection is therefore the key point for selecting coulomb excitation events. In particularin the experiment here discussed the minimum distance for coulomb excitation events
correspond to a maximum scattering angle of ∼ 11 mrad (the so called, grazing angle).
As explained in the previous section, the experimental uncertainity on the scattering angle is of the order of 2 mrad: this has as a consequence that a gate on 11 mrad does not
exclude events with larger scattering angle and therefore with smaller minimum distance approach between projectile and target.
For this reason a more strict condition has to be applied to the scattering angle. In theanalysis a gate of 8 mrad was chosen. This value corresponds to a distribution of minimum distance peaked around 17.5 fm, but it ensures that a percentage lower than 10%of the total events are characterized by a minimum distance approach lower than the
nuclear interaction range.
This choice of a selection of small scattering angle had as a consequence that only theions hitting the two central DSSSD panels, where the statistics was mainly distributed,
were considered. The very few statistics in the panels around could have increased more
the background, including spurious ion trajectories, than the events we were interested
in.
This section of the data analysis demonstrated that the PreSPEC setup was correctly
tuned for coulomb excitation investigation at relativistic energies.
In conclusion, the analysis of the LYCCA array detectors allowed to define the gates on
E-∆E matrix to select the same projectile 62,64 Fe(see Fig. 4.11). In addition we use LYCCA to select the scattering angles lower than 8 mrad (see Fig. 4.14): this angle choicecorresponds to consider coulomb scattering events with a minimum impact parameterof 17 fm( A more detailed discussion of the choice of this value will be presented in
Chapter 5).
The next step of the data analysis: the γ ray spectra investigation, was performed after
applying these two gates.

4.3 PreSPEC-AGATA data analysis: Gamma ray detection

76

Figure 4.14: Angular scattering distribution in mrad of ions detected with forward Wall DSSSD
panel. In blue the accepted angles.

4.3

PreSPEC-AGATA data analysis: Gamma ray detection

4.3.1

AGATA

Calibrations and settings
The AGATA data were ”replayed” using Femul emulator and prespec code (for more details see App. C). The former was used, as a first step, to apply calibrations, alignements
and PSA filter. The latter to merge AGATA data with MBS data that represent the datafrom all the other detector systems. The last step of AGATA data processing consisted
in the application of the tracking algorithm. MGT libraries were used, after a fine tuningof the parameters and the threshold of the figure of merit.
Before the experimental campaign an high precise measurement of detector position
was performed by J. Strachan et al. with a laser system. These positions were used
as references for AGATA detectors. This required a geometrical transformation of thepositions of AGATA crystal as implemeted in analysis codes available. In Fig. 4.15 theposition of detectors as implemented in the code are represented in comparison with themeasured positions (black crosses). A rotation of 7.5 degrees was needed to make crystal

Chapter 4: Data Analysis

77

positions in the code equal to the ones measured.
The γ-ray energy calibrations were performed using 60 Co and PuC sources. In the two

Figure 4.15: Left panel: the comparison between the position of crystal measured before the campaign(black crosses), and the position of crystal in the analysis code. Right panel: the same comparison after the rotation to correct the positions in the code

panels of Fig.4.16 the energy spectra from these two γ-ray sources are shown. The energy
range required in the measurement spanned from 1 MeV till 15 MeV as not only PDR
gamma decay need to be measured, but also the gamma decay from the first 2+ of theexotic ions: the latter is important for the normalization needed to extract the strengthof the PDR. References [51], [50] verified the linearity of AGATA on all the energy range
of interest.
Energy resolution for the AGATA crystal was checked with calibration source: a valueof FWHM < 3 keV was obtained for peaks at the energy of 1 MeV. Two crystals (12C
and 14A) showed a worse energy resolution due to a larger contribution of noise in fact
the increase in ∆E
E was not proportional to the energy but it remained approximately
constant. For this reason these detectors were not excluded in the data analysis: in fact
the doppler broadening expected was much higher than the HPGe detector intrinsic
energy resolution.
The ion-γ time (here denoted as particle-γ time) was obtained as:
TP −G = Tγ − Tpart(4.7)

Both time for gammas and ions were referred to the trigger of the acquisition. This signal
was produced by the FPGA responsible of the coincidence and triggering of the system.
Therefore particle-gamma time can be rewitten as [74]:TP −G = (Tγ − Ttrigger )T imestop − (Tpart − Ttrigger )T imestart(4.8)

Tpart is obtained by the scintillator on the last FRS focal plane (SC41), while Tγ is ob-

78

4.3 PreSPEC-AGATA data analysis: Gamma ray detection

Figure 4.16: On left panel 60 Co source energy spectrum for calibration. On right panel PuC sourceenergy spectrum for calibration: peaks at low energy are related to backround.

tained by the leading edge of the signal of HPGe detectors. For this reason the EnergyTime matrix of these detectors is characterized by a significant Time-Walk (left panel of
Fig.4.17). It is possible to apply Time-Walk correction, in order to avoid this phenomenon(right panel of Fig.4.17).
In Fig.4.18 the time spectrum of one crystal was shown after the Time Walk correction
and alignement to zero value. The time resolution of each crystal was estimated in therange from 16 to 30 ns. The timing resolution of all AGATA detector system was measured as 24 ns.
Time resolution, at fixed γ-ray energy, was measured after and before the Time Walk correction: a no significant difference in the two cases was obtained. For this reason, in thesubsequent analysis, timing conditions were applied using proper cuts on Energy-Timematrix. This allowed to avoide the possibility of introducing some bias induced by theTime-Walk correction or by the alignement of timing of the crystals.
The doppler correction at high β values requires a precise determination of the angle
between the projectile direction and the γ-ray emitted. As described in previous section
ion tracks are recostructed using stripped silicon detectors (DSSSD), this provide a precision of the order of 1 mm. Gamma ray tracking algorithms provide the direction of γs
detected by AGATA. The tracks are reconstructed using position determination obtainedwith PSA. The resolution in measuring the position is of the order of 5 mm. These consideration shows that the setup allows to get an high precise determination of the angle
for doppler correction. It is important to have also the relative position of γ-detectors
and ion tracking panels.

Chapter 4: Data Analysis

79

Figure 4.17: On left panel the Time-Energy Matrix, on y-axis time in ns and on x-axis energy in
keV.On right panel the Time-Energy Matrix after the Time Walk correction and alignement

Figure 4.18: Time spectrum for an AGATA crystal after Time Walk correction and alignement.
FWHM obtained : 17.8 ns

The relative position of the target with respect to the γ detectors was checked and fixedduring the analysis of these data. It was found in fact that an offset of a few millimeters
was needed.
The measurement and the simulation of the AGATA efficiency are described in App. B.
A good agreement between the measurement and the simulation was obtained. The efficiency at 1 MeV of ∼3%, obtained by the source calibration runs, is in good agreementwith the value published in the thechnical reports (3.25% at 1 MeV) [75].
Gates and filters
In order to obtain the spectrum of the gamma ray emitted in the interaction with thetarget, the conditions, explained below, on time and gamma ray tracking algorithms

4.3 PreSPEC-AGATA data analysis: Gamma ray detection

80

Figure 4.19: Left panel, time projection of Energy-Time gate at energy 0.5-2 MeV (ns on x-axis).
Right panel, time projection of Energy-Time gate at energy 7-25 MeV (ns on x-axis)

were applied.
The gates on Energy vs Time matrix were applied for all the crystals to select prompt
gammas from the target. In the two panels of Fig.4.19 the time spectra in two different
energy range and the gates applied are represented. As displayed in the figure, thewidth of time gates is of the order of 20 ns; this is consistent with the FWHM of time
peak dispalyed in Fig. 4.18.
Low energy gamma ray spectra were affected by a significant background contribution, coming probably from the target frame and from the materials around the target
or along the beam line. For this reason, the gamma ray spectra in the region of 0.5 - 2
MeV were obtained applying MGT libraries for gamma ray tracking with a very restrictive condition on the figure of merit (see discussion in 3.1.3). In fact a Figure of Merit of
0.1 was required to accept the gamma ray reconstruction. In case of γ rays with Eγ >2
MeV the background resulted to be less intense and therefore less restrictive conditions
on gamma recontruction were required. In addition a different tracking algorithm wasused. The algorithm here applied reconstructed the energy of the gamma rays summing
all the interaction points around the position of the most energetic release. This choice isdue to an higher efficiency of gamma ray tracking in the range of 6 - 15 MeV [51] (25%or more than MGT tracking algorithm).
4.3.2

HECTOR+

HECTOR+ data, as anticipated before, were embedded in MBS system. In the data analysis, only the LaBr3 spectra were considered and will be displayed as BaF2 scintillators
being at the backward angles, collected very low statistics,which indicates very low highChapter 4: Data Analysis

81

energy background from the target for our region of interes. The energy calibration was
performed using the same calibration sources of the AGATA array. In Fig. 4.20 an exemplum of the spectrum measured with PuC source is plotted.
The intrinsic time resolution of LaBr detectors is 500 ps but once mounted in the experi-

Figure 4.20: Energy calibration spectrum with PuC source.

ment it was estimated in the order of around 2 ns due to long cables of up to 35m needed
to insert these detectors in the setup. In Fig.4.21 the time-energy matrix is displayed. It
is possible to see a delayed structure around channel 820, approximately 20 ns later thanthe prompt peak which is at channel 800. This is a signature of a delayed backgroundcontribution: probably coming from the γ flash generated by the hit of the beam in LYCCA detectors.
The prompt peak at high energy is also more broadened than at low energy one, as it canbe seen in Fig. 4.22, where the time spectra in the low and high energy range are plotted.
The timing resolution at higher energy seems worsen but on the other hand the spectrum is more clean. In these two spectra the gates applied to obtain the γ ray spectra areshown: 2 ns and 3 ns time window gates were applied respectively in the low (Energy <4 MeV) and high energy range (Energy > 4 MeV).
As explained in chapter 3, LaBr3 :Ce detectors are affected by the internal radiation.
In the case of this large volume detectors, a rate of 1kHz is expected for the 1461 keV
peak. Considering that at this energy the time window is 2 ns and statistics and triggers
registered in these experiments, 13 counts per crystal are expected for the 2012 setup
while only 8 counts for the 2014 setup. Therefore the background induced by internal

82

4.3 PreSPEC-AGATA data analysis: Gamma ray detection

Figure 4.21: Time-Energy matrix for a LaBr detector. Energy in keVs on y axes and time in ns on x
axes.

Figure 4.22: Left panel, time projection of Energy-Time gate at energy 0.5-2 MeV (ns on x-axis).
Right panel, time projection of Energy-Time gate at energy 8-30 MeV (ns on x-axis)

radiation is negligible.
In conclusion this section showed that AGATA γ ray energy spectra were obtained after
applying a time gate of the order of 20 ns, while the time window for LaBr was of theorder of 2-3 ns. The limit of the Figure of Merit of tracking algorithms was fixed at 0.1
for the low energy range, because of the high level of the background. No conditions on
multiplicity were applied: it was observed that the measurement was characterized bylow multiplicity, infact after the gates, explained here and in the previous sections, thenumber of events with multiplicity higher than 2 was not significant, as shown in fig.
4.23.

Chapter 4: Data Analysis

83

Figure 4.23: Multiplicity of AGATA crystals with the gates described in this and previous sections

4.4

PreSPEC-AGATA data analysis: Final Gamma ray spectra

The final AGATA and HECTOR energy spectra were obtained after applying all thegates listed in the previous sections. In particular AGATA and LaBr3 :Ce spectra wereconstructed using the following gates:• Incident secondary beam of 64 Fe (or 62 Fe)• After the secondary target outcoming beam of 64 Fe (or 62 Fe)• Gate on scattering angle of the beam for Coulomb excitation selection
For AGATA:• Time gate of ∼20 ns on time γ-particle where S4 scintillator is the start and AGATA
crystals the stop
• Tracking with MGT libraries using FoM < 0.1 (Eγ <2 MeV)
• Tracking with a bubble algorithm for Eγ >2 MeV• doppler correction using event by event calculation of β
For LaBr3 :Ce :• Time gate of 3 ns for Eγ <4 MeV

4.4 PreSPEC-AGATA data analysis: Final Gamma ray spectra84• Time gate of 4 ns for Eγ >4 MeV• doppler correction using event by event calculation of β
Fig. 4.24 and Fig.4.25 show the AGATA spectra in low and high energy range respectively.

The low energy spectra show a peak at the energy of the first 2+ state decay

Figure 4.24: Panel a): the low energy spectrum measured with AGATA for 64 Fe coulomb excitation
events.Panel b): the low energy spectrum measured with AGATA for 62 Fe coulomb excitation
events.

Figure 4.25: Panel a) the high energy spectrum measured with AGATA for 64 Fe coulomb excitation
events. Panel b): the high energy spectrum measured with AGATA for 62 Fe coulomb excitation
events.

for both projectiles. 64 Fe level scheme [76], shows a 2+ state at 746 keV while the level
scheme for 62 Fe [77], has a 2+ state at 877 keV. This is an important point for the E1
measurement. Thanks to the fact that the B(E2) strength of the first 2+ state decay forboth of the ions is known, the statistics in the peaks related to this decay will provide theChapter 4: Data Analysis

85

normalization for the E1 cross section, essential to deduce B(E1) values for high energy
measured strength.
High energy spectra produced by 64 Fe and 62 Fe show some structures in the energy
range of 6-8 MeV. A simple argument to prove that these structures are neither statis-

Figure 4.26: Panel a): the low energy spectrum (black) measured with AGATA for 64 Fe comparedwith a simulation (grey) of in-flight emission of 746 keV gammas. Panel b): the low energy spectrum (black) measured with AGATA for 62 Fe compared with a simulation GEANT montecarlo(grey) of in-flight emission of 877 keV gammas.

Figure 4.27: The high energy spectrum (black) measured with AGATA compared with a simulation (grey) of in-flight emission of 5 MeV gammas.

tical fluctuations of background nor generated by artifacts of the data analysis, is thecomparison with simulations. A GEANT4 simulation (for more details see App. B), wasperformed to obtain the expected spectra of AGATA for this measurement. The emission
from the projectile of γ-ray at energy 746 keV, 877 keV and 5 MeV was simulated. In Fig.

86

4.4 PreSPEC-AGATA data analysis: Final Gamma ray spectra

4.26 and 4.27 the comparison between the simulation and the experimental spectra isshown: the width and the line shape of the structures of interest at low and high energy
are consistent with the expected ones from the simulations.
In the next chapter there will be a more detailed discussion about the statistics in theenergy spectra, in particular in the range of 6 - 8 MeV.
The HECTOR+ spectra have a too low statistics to allow the observation of the low energy 2+ peak transition. In Fig. 4.28 the spectra for the two ions are plotted: only forward
angle detectors are considered. This choice is due to the fact that the background contribution from target excitations is smaller at forward angle due to the lorentian relativistic
boost. The reason of this difference in statistics respect to AGATA spectra is mainly connected to the smaller solid angles covered by LaBr3 detectors with respect the AGATA
array and the angular position of the detectors. In addition the worse energy resolution
and the higher doppler broadening respect to AGATA crystals require higher statistics
to make peak structures at high energy prevail on the background.

Figure 4.28: Left panel, the high energy spectra measured with LaBr at 68o for 64 Fe coulomb
excitation (LaBr at 22o were missing in the setup); right panel, the high energy spectra measured
with LaBr at 22o for 62 Fe coulomb excitation.

Chapter 4: Data Analysis

4.5

87

DALI2-HECTOR+ data analysis: identification and selection of
the ions

In Riken laboratory the identification and the selection of the radioactive ion beam is
performed using the Big-Rips magnetic separator. As explained in the previous chapter, this identification is obtained by the estimation of the magnetic rigidity of the beamand the measurement of energy loss in the ion chambers. The Big-Rips team provides
the calibration coefficients for all the detectors on the beam-line. These coefficients are
determined for every experiment in order to take into account drifts in the gain of thedetectors or changes in the settings. This allows to get high accurate Z vs A/Q plots.
In Fig. 4.29 the Z vs AoQ plot for 70 Ni is shown, these are the equivalent of fig 4.7 obtained for GSI data the ions are very well separated, as a consequence the selection of70

Ni events includes very low background as compared with GSI data.

The red circle in Fig. 4.29 shows the gate applied on this matrix to select the ions impinging on the secondary target: all the following data analysis was performed after
applying this condition.

Figure 4.29: Identification plot obtained with Big-Rips magnetic separator: A/Q on x axes and Z
on y axes. The 70 Ni bump is well separated and the most intense one. The red circle represents thegate on the matrix to select 70 Ni beam.

88

4.6 DALI2-HECTOR+ data analysis: Coulomb excitation events selection

4.6

DALI2-HECTOR+ data analysis: Coulomb excitation events selection

The Zero Degree Spectrometer was used to select outcoming ions after the secondary
target. As in Big-Rips, the identification is obtained measuring the magnetic rigidity of
the ions. An accurate calibration of the detectors on the beam line is therefore needed:
this was performed by the ZDS team at the beginning of the experiment. In fig.4.30 the
Z vs A/Q plot is shown. As for the ions incoming on the secondary target, the bumps
related to the ions are well separated, this means that also the selection is very clean, as
represented in Fig.4.30 where the red circle represents the gate applied for outcoming
70

Ni, this is the equivalent of Fig. 4.11 for GSI data.

The scattering angle is measured using the PPACs before and after the target (detectors
placed at F8 focal plane). The angular sensitivity is lower than in PreSPEC experiments:
here the uncertainity is of the order of 5 mrad. In addition, the lower beam energy incomparison with GSI experiment, makes the angular straggling in the target more important. The consequence is that, in this case, it is not possible to select pure coulomb
excitation events. For this reason the interpretation of γ ray spectra measured will consider both coulomb and nuclear interaction.
Fig. 4.31 shows the selection applied on the scattering angle, the gate accepts scattering
angles smaller than 28 mrad that corresponds to an impact parameter of 13 fm.
In conclusion, Fig.4.30 and Fig.4.31 shows the gates applied to select mainly coulomb
excitation events for 70 Ni, even if, as explained before excitations via nuclear interaction
were not excluded; the data analysis of γ ray spectra was performed after having appliedthese gates.

Chapter 4: Data Analysis

89

Figure 4.30: Identification plot obtained with the Zero Degree Spectrometer: A/Q on x axes andZ on y axes. The 70 Ni bump is well separated and the most intense one. The red circle represents
the gate on 70 Ni.

Figure 4.31: Scattering angle distribution. The filled area indicates the angles selected

4.7

DALI2-HECTOR+ data analysis: Gamma ray detection conditions

As explained in the previous chapter, the γ detection was performed with NaI and
LaBr3 :Ce scintillator detectors. The energy calibration was performed using 60 Co,90 Y,137 Cs
and Cm-C sources. It was important to have good calibration in both the high and low

90

4.7 DALI2-HECTOR+ data analysis: Gamma ray detection conditions

energy range: as in GSI experiments, it is important to measure both first 2+ state decay
and the high γ-ray energy transitions. In order to avoid possible gain drifts in NaI scintillators during the measurements, the calibration runs were performed before and after
the production runs. In Fig. 4.32 the matrix with all NaI scintillator calibrated spectrais shown, while in Fig. 4.33 a superimposition of LaBr spectra with calibration source isplotted. The particle-γ time was obtained by the difference between the time signal of

Figure 4.32: Left panel: matrix built with DALI2 detector energy spectra acquired with 60 Co
source. Right panel: matrix built with DALI2 detector energy spectra acquired with Cm-C source.

Figure 4.33: Left panel: LaBr energy spectra acquired with 88 Y source. Right panel: LaBr energy
spectra acquired with Cm-C source.

DALI2 or LaBr3 :Ce scintillators and F8 plastic scintillator. The timing corresponding toγ signals was produced using a CFD (see Fig. 4.34). As shown in fig.4.35, the time gateapplied for LaBr3 :Ce was of 4 ns while the time gate for NaI was of 5 ns. The LaBr3 time
resolution above 2 MeV was, as can be seen in figure 4.34 right panel, around 2ns.
Nevertheless a 4ns gate has been used in order to take also the low energy part inside
the trigger.
Recently a preliminary review of the data reduction code of RIKEN is under development, but will not be fully debugged before mid 2016, where additional corrections on
positions and ppacs pin down the timing resolution of the system, which means that theChapter 4: Data Analysis

91

overall time resolution of the LaBr scintillators are around 1.5ns.

Figure 4.34: Left panel: DALI matrix with the timing spectra of all detectors. Right panel: exemplum of energy-time matrix for LaBr detectors.

As regarding the internal radioactivity, in this setup and with these time gates the
expected counts related to the 1461 keV peak are of the order of 800 counts per crystal.
In order to obtain, as much as possible clean γ ray spectra, the time gates explained

Figure 4.35: Left panel: NaI time spectrum, the filled area display the time gate applied. Rightpanel: LaBr3 time spectrum, the filled area display the time gate appliedabove and shown in Fig.4.35 were applied. In addition the energy spectrum measuredout of the gate on the prompt peak was subtracted to the prompt energy spectrum , after
an appropriate normalization. In this way not time correlated events were removed.
As in GSI experiment, the multiplicity of γ detected was low, for this reason no multiplicity gate was applied.

4.8

DALI2-HECTOR+ data analysis: Final spectra

Final γ ray spectra were obtained with a gate on impinging ion (70 NI) on the secondary
target (see section 4.5), the gates on outgoing 70 Ni (see section 4.6) and on γ prompt time(described in section 4.7).
Fig. 4.36 shows the LaBr3 spectrum at low energy: the peak corresponding to the energy

4.8 DALI2-HECTOR+ data analysis: Final spectra

92of the first 2+ state decay [78] prevails clearly on the background.
Fig. 4.37 shows the energy spectra measured with DALI2 array at different angles: it ispossible to see how the 2+ state peak is not visible in backward detectors. This is due tothe fact that the Lorentz boost makes the projectile γ emission focused at forward angles,
as a consequence at backward angles the γ emission from the projectile is less intense.
For this reason the spectrum of backward detectors mainly measure target γ emission ortime correlated background.

Figure 4.36: 70 Ni energy spectrum measured with LaBr detectors

Figure 4.37: 70 Ni energy spectrum measured with DALI2 detectors: the left panel shows the energy spectrum measured by forward layer detectors (45o -75o ); the central panel shows the spectrum measured by central layer detectors (75o -105o ); the right panel the one measured by backward layer detectors (105o -150o )Chapter 4: Data Analysis

93

Fig. 4.38 shows the high energy spectra measured with LaBr3 detectors. The plot
evidence an unresolved structure just below the particle threshold (Eγ ∼ 7.5 MeV) andsome structures above the threshold. In fig.4.39 the same structure below the particle
threshold is visible in the spectrum of forward layers, backward layers spectrum does
not show the same structures because of the less intense projectile emission.

Figure 4.38: 70 Ni energy spectrum measured with LaBr3 :Ce detectors: the left panel shows theunresolved structure below the one particle separation energy (5-7 MeV); the right panel shows
the structure above the threshold.

Figure 4.39: 70 Ni energy spectrum measured with DALI2 detectors: the left panel shows the spectrum in the high energy range measured by forward layer detectors (45o -75o );the right panel shows
the spectrum in the high energy range measured by backward layer detectors (105o -150o )C HAPTER 5

Discussion of experimental results

In this last chapter the experimental spectra obtained at the end of the previous chapter
will be analyzed and discussed. In particular, the estimation of B(E1) values of γ-ray
transition at energies just below one particle separation energy, will be discussed.

5.1

Beam correlated background evaluation

In GSI data analysis, two different approaches were combined to have an evaluation of
background contribution in AGATA spectra in 6-12 MeV energy range (in the projectile
frame). In one case we used LaBr3 scintillators, in the other case AGATA spectrum itself
was used.
Background evaluation with LaBr3 scintillators
One of the advantages of PreSPEC setup described in the previous chapter, is the angular
positions of high efficient scintillators. Energy spectra measured with backward detectors are mainly affected by beam correlated background contributions. As large volume
scintillators have an efficiency higher than an AGATA crystal for high energy γ rays, it
is possible to evaluate the background induced by the beam for γ energy between 10-20
MeV (in the laboratory frame), corresponding to 6-12 MeV in the projectile frame.
The estimation of background was done comparing the energy spectrum of the scintillators backward and forward angles. This analysis showed a flat and very weak contribution of the background in the energy region of interest (6-12 MeV in the projectile frame).
The fig. 5.1 shows the shape of the LaBr3 spectrum (after doppler correction) used to get
the evaluation of the background. As already stated, it is very weak (few counts only).
In the energy window 7-12 MeV it is flat and for energy larger than 12 MeV is negligible.
95

96

5.1 Beam correlated background evaluation

It was not possible to use the beam correlated background extracted from scintillators

Figure 5.1: Shape of the energy spectrum from LaBr3 scintillators after the application of the typical doppler correction in AGATA, to evaluate background contribution in energy region of interest

directly in AGATA spectra. In fact these detectors have different response function.
Therefore the scintillator spectra were ”transformed” in AGATA spectra using the response function obtained by simulations (for more details see App. B).
The statistics collected in the peak related to the de-excitation of the first 3− level oflead target was used to normalize the response of the two detector systems: AGATA
and LaBr3 :Ce array. The two panels of Fig. 5.2 show the energy spectrum measured
with AGATA and with a LaBr3 scintillator. The different energy resolution is evident, in
terms of counts the statistics in the peak in the two spectra are comparable. This comparison had as a result a normalization factor of 1.5 between LaBr3 and AGATA detectors.

Background evaluation with AGATA
The second approach used to get an evaluation of background is based on the hypothesisthat counts at Eγ >15 MeV comes from background only. Therefore the evaluation of thebeam correlated background in the energy range 6-12 MeV was obtained scaling for thearray efficiency. Fig. 5.3 shows the beam correlated background level obtained with thisapproach. As in the case of the background evaluation performed using the scintillators,
the background is structureless and very weak in the energy region of the one particle

Chapter 5: Discussion of experimental results

97

Figure 5.2: Left panel: exemplum of AGATA spectrum for 3− level decay of 208 Pb. Right panel:
exemplum of LaBr spectrum for 3− level decay of 208 Pb.

separation energy (6-12 MeV).
The approach using the scintillators provided an higher background level than the one

Figure 5.3: Energy spectrum measured with AGATA: the binning is equal to 1 MeV. The red line
represents the background obtained with the statistics around 20 MeV. The thickness is related tothe propagation of the statistical error in the high energy region.

obtained using AGATA statistics, almost twice bigger. The low level of the backgroundmakes the difference of result of these two approach not relevant. In the next step of theanalysis the squared average of the backgroound level obtained with these two methods
will be considered and subtracted to the AGATA spectrum.

5.2 Normalization of the cross section

98

5.2

Normalization of the cross section

The estimation of an absolute cross section represents the precise knowledge of deadtime, algorithm dependant efficiency, background sources, pile up events and so on.
For this reason it is a typical approach to rely on a known transition measured within
the same experiment with exactly the same conditions.
The key point in this approach is the normalization factor between the reference known
transition (in this case the decay from 2+ state) and the unknown one (in this case thedecay of the PDR).
As shown in the spectra 4.24, the setup allowed to measure the first 2+ state decay for62

Fe and 64 Fe.

In particular the statistics measured for these transitions was compared with the statistics expected considering the B(E2) values reported in literature (table 5.1): in the following paragraph a description of the approach used for this estimation is presented.
The B(E2) values used in this data analysis and adopted by NNDC database, are consistent with the measured values for 62 Fe ( [81], [82]). The value adopted for 64 Fe isconsistent with the experimental value measured via coulomb excitation in [81]. Another value is avaible in literature about B(E2) for this nucleus [82], but it is out of thesystematics of neighbouring nuclei and we have decided not to consider it.
The cross section for 2+ state excitation was computed using the relation [79]:6462EnergyB(E2)Fe

746 keV1780 e2 mb2Fe

877 keV1028 e2 mb2

Table 5.1: Energy and B(E2) values for the first 2+ state peak for both the ions [80]

"
#

2
 c 48π 2 ZT2 α 2
2 2
1
v4 ξ2 22σE2 =E B(E2)× 2 K1 + ξ 1 + 2
K0 K1 −
(K1 − K0 )
75 (~c)3 x
v
γ
γ
2c4
(5.1)
where K are modified bessel functions of the parameter ξ =ωf i Rγv , with E = ~ωf i is theexcitation energy and R is the minimum distance, corresponding at minimum impact
parameter in relativistic regime (in this data analysis R= 17.5 fm).
Using the well known experimental definition of cross-section and the gamma detection
efficiency estimated with the simulations described in B, the number of gammas emitted

Chapter 5: Discussion of experimental results

99

from the 2+ state decay and detected by AGATA was estimated.
Nexpected = Np NT σ

(5.2)

where  is the absolute detector efficiency, Np the number of the projectiles and NT thenumber of nuclei in the target. This value need to be corrected considering the angular
distribution for the E2 emission due to the doppler boost. In fig. 5.4 a comparison between the spherical emission, the E1 and E2 emission after Lorentz boost is displayed.
DWEIKO [93] code was used to get this evaluation.
The result of this procedure was compared with the statistics collected in the measured

Figure 5.4: The angular distributions after Lorentz boost. Black line shows the angular distribution
for spherical emission, the blue one for dipole emission and red one for quadrupole emission.

photopeak. The ratio provided the following normalization factors:= 0.5 ± 0.1 for 64 Fe
Nsc = NNmeasured
expected
Nsc = NNmeasured= 0.55 ± 0.1 for 62 Fe
expected
The factors summarize the effect of dead-time, background systematic errors, geometrical setup, non idealities. The two values are very similar, in fact the 2014 setup was
tuned to be similar to the one used in 2012.
The error on this value was obtained considering the poisson error on the statistics collected for this transition and the uncertainty on the expected value, due to the experimental errors on the parameters used for this calculation.

100

5.3 Gamma yield contribution from GDR decay in pygmy energy region

5.3

Gamma yield contribution from GDR decay in pygmy energy region

We discuss here the γ yield contribution of GDR in the energy range of 6-10 MeV in order to compare it with the spectrum measured with AGATA. In next sections it will beshown that the experimental spectra have an amount of statistics higher than the one
expected for the background and for the GDR γ decay. It is important to remember thatthe experimental conditions applied in the GSI data analysis described in the previous
chapter select almost pure coulomb excitation events for 64,62 Fe.
As discussed in 4.2.3, the selection on scattering angle reduced the statistics related tonuclear excitation to a percentage lower than 10% of the amount of statistics considered in the last steps of the data analysis: therefore the contribution of nuclear excitation
mechanism can be considered included in the error bars.
As explained in chapter 2, the coulomb interation at relativistic beam energy is dominated by dipole excitation. The energy spectrum of the virtual photons related to dipole
interaction can be obtained by the relation:v2 ξ2 2
2Z 2 α c 22( ) ξK0 K1 −(K−
K)
NE1 (Eγ ) =
1
0
π
v
2c2

(5.3)

where ξ = ωDγv .
This is an approximation of the relations described in 2.2.
The experimental conditions of the measurement here discussed (D=17.5 fm and β ∼0.71) provides an adiabatic cutoff in the range of 10-12 MeV. However the exponential
tail of the distribution reaches the energies expected for GDR.
The electromagnetic excitation cross section can be obtained by the relation:X
X Z dEγ
πλ
σC =
σC
=
Nπλ (Eγ )σγπλ (Eγ )
Eγ
πλ

(5.4)

πλ

where σγπλ is the photoabsorption cross section for a parity π and angular momentum λ.
In the case of GDR, it can be written as:Z
dEγ
σexc =
NE1 (Eγ )σGDR (Eγ )
Eγ

(5.5)

where σGDR (Eγ ) is the GDR photoabsorption cross section. In the case of the Iron isotopes here discussed, no experimental values are available for the GDR photoabsorption
cross section. For this reason the parameters from RIPL-3 database were used [87]. RIPL
database expects a splitting of GDR as showed in the table below, it was supposed an

Chapter 5: Discussion of experimental results

101

Z

A

El

Eta

E1[MeV]W1[MeV]E2[MeV]W2[MeV]

26

64

Fe

1.161

16.80

4.96

19.27

8.42

26

62

Fe

1.161

16.95

4.78

19.45

7.89

Table 5.2: GDR parameters predicted by RIPL database. E1 and W1 are the centroid and the widthof the first peak while E2 and W2 are thecentroid and the width of the second peakequal amount of the strength for the two components. The strength related to GDR was
estimated using the TRK sum rule, exposed in Chap. 1.
Therefore 5.5 can be used to obtain the excitation cross section for GDR.
The relation:
Nexc = Np NT σexc

(5.6)

shows that knowing the number of projectiles (NP ), the number of target nuclei (NT )and the excitation cross section, it is possible to obtain the number of excitations expected in a measurement.
Fig. 5.5 shows the excitation cross section spectrum for 64 Fe analysis, the thick band isdue to the variation of the excitation probability in relation to the spread in the minimum
impact parameter.

Figure 5.5: Energy excitation spectrum used as input of the GEMINI code for 62 Fe analysis (leftpanel) and 64 Fe analysis (right panel).The thick band is due to the variation of the excitation probability in relation to the spread in the minimum impact parameter.

The γ yield of GDR decay was evaluated using GEMINI code [86] , [85]. This code
computes the statistical decay of an excitated Compound Nucleus, taking into accountall the possible mechanisms of de-excitation. This code is more extensively explained in5.3 Gamma yield contribution from GDR decay in pygmy energy region

102

App A.
The excitation spectrum showed in 5.5 was used as input for the code. The output of
GEMINI for γ emission decay mechanism is shown in Fig. 5.6.
In order to compare this γ spectrum with the experimental one, it was folded with the
AGATA response function.
In fig.5.6 the spectra in C.M. system obtained as output of GEMINI for 62 Fe and 64 Fe
analysis are shown. In fig.5.7 the same spectra of Fig.5.6 but folded with AGATA response function are shown.
Using the same technique, also target excitation yield was evaluated. In this case the

Figure 5.6: GEMINI output γ spectrum for 62 Fe (left panel) and for 64 Fe (right panel).

Figure 5.7: γ yield for 62 Fe analysis of the experimental spectrum(left panel) and for 64 Fe analysisof the experimental spectrum(right panel).

RIPL database provided experimental values for the GDR parameters (see table 5.3).
Also here the emission spectrum was folded with AGATA response function, in addition

Chapter 5: Discussion of experimental results

103

Z

A

El

E1[MeV]

CS1[mb]W1[MeV]

82

208

Pb

13.63

643.7

3.93

79

197

Au

13.73

501.1

4.74

Table 5.3: Experimental parameters for GDR in 208 Pb [88] and in 197 Au [89].

(even if wrong) the doppler shift relative to the projectile was applied in order to compare the spectrum with the experimental one: in this case infact the emmission source isat rest respect the detectors.
The γ yield from GDR decay of the projectile was summed to the one of the target toobtain the yield on the all energy spectrum, see Fig. 5.8.

Figure 5.8: γ yield from GDR decay of the projectile and the target for 62 Fe analysis (left panel)and for 64 Fe analysis (right panel)

5.4

Spectra subtracted and multipolarity investigation

Fig. 5.9 shows the experimental spectra for both Iron isotopes compared with the γ yield(red line) coming from GDR decay and background. The thickness of the red line represents the uncertainity due to statistical and experimental error bars. These reported
spectra clearly show an amount of statistics higher than background namely related tothe tail of the GDR.
The subtracted spectra in fig. 5.10 show the structures remaining after the subtractionof the background and GDR γ yield. These structures were considered as the decay of
E1 excitations. The reaction mechanism used in these experiments, explained in chapter
2, selects practically only dipole excitation.

104

5.4 Spectra subtracted and multipolarity investigation

Figure 5.9: AGATA energy spectrum compared with the γ yield from GDR decay and backgroundfor 62 Fe analysis(left panel) and for 64 Fe analysis(right panel).

Figure 5.10: AGATA energy spectrum after the subtraction of the γ yield from GDR decay andbackground for 62 Fe analysis(left panel) and for 64 Fe analysis(right panel). In both figures theenergy range that will be considered for the estimation of B(E1) values is underlined by a red
shadow.

In fig.5.11 the cross sections related to E1 and E2 excitations in 6-10 MeV energy range
are shown at different beam energies, the B(E1) and B(E2) values used for this calculation are taken from [90], [91] . It is clear that the cross section related to E1 transitions ispredominant respect to the one related to E2 transitions.
Though the statistics was very low, an angular investigation was performed. For thisreason, an incremental angular distribution was considered. This means that at every
angle, all the statistics from 0 rad till the value considered was summed.
Fig.5.12 shows the ratio of the incremental angular distribution between the first 2+ decay peak and the statistics in 5-8 MeV range. The experimental points are compared with

Chapter 5: Discussion of experimental results

105

Figure 5.11: Circle points represent the cross section for an E1 transition in the experimental setting
here used, while squared points represent the cross section for an E2 transition.

the expected trend obtained folding the E1 and E2 distribution plotted in fig. 5.4 and the
AGATA response function. As comparison, the same cumulative angular distribution isplotted for the ratio of the 2+ state decays of the two ions.
It is possible to see that the distributions in the two conditions have a different trend.
If we consider just these two diagrams by their own this is not a sufficient proof to assign the multipolarity of the high energy statistics. Anyway they clearly show that the
cumulative angular distribution is different in the two cases, this is a strong indicationthat the high energy statistics cannot be assign completely to E2 transition. Nevertheless,these diagrams coupled with the previous consideration about the cross section, provide
a very clear indication that the structures in the subtracted spectra are related to E1 transitions.
In conclusion, it was shown that an amount of statistics between 6 and 8 MeV remains
in the spectra after the background subtraction (Fig. 5.10). This spectrum was obtained
after the selection of an incoming and outcoming 62,64 Fe beam, in addition coulomb excitation mechanism was selected. The coulomb excitation at relativistic beam energy
selects dipole excitation: infact the comparison of the angular distribution of this highenergy statistics with the angular distribution of the first 2+ state decay, showed that themultipolarity is different from E2.

5.5 E1 investigation in 70 Ni isotope

106

Figure 5.12: Left panel: ratio between the cumulative angular distribution associated to the 2+
decay events and the one in the range 5-8 MeV, compared with the expected trend for the E2/E1
and E2/E2 ratio. The expected trend were obtained considering the experimental setup. Rightpanel: cumulative angular distribution for the ratio between the cumulative angular distribution
associated to the 2+ decay events in 64 Fe and in 62 Fe, compared with the expected trend for theE2/E1 and E2/E2 ratio.

5.5

E1 investigation in 70 Ni isotope

A procedure similar to the one used to investigate the E1 strength in GSI was applied for70

Ni.

The cross-section normalization factor was not obtained by the 2+ decay level because
there is a significant disagreement in the values already in literature between measurements and theory for 70 Ni and between the different thoretical results in 72 Ni [95]. For
this reason and considering the high statistics here collected, the absolute peak strength
determinated in this work will be used in the following data analysis to get an estimation of its B(E2) value.
The cross-section normalization factor was therefore obtained in another experiment(about pygmy in Oxigen ions) with the same setup [94]. The value used in this analysis was equal to 0.9.
As introduced in the previous chapter, the uncertainty on the precise scattering angle
measurement makes the contribution of nuclar excitation events relevant in this data
analysis.
According to Reference [96], the nuclear contribution in this measurement is rather small,namely 20% of the events.
In the following discussion the statistics selected with the gates described in the previ-Chapter 5: Discussion of experimental results

107

Z

A

El

Eta

E1[MeV]W1[MeV]E2[MeV]W2[MeV]

28

70

Ni

1.

18.02

6.73

18.02

6.73

Table 5.4: GDR parameters predicted by RIPL database. E1 and W1 are the centroid and the widthof the first peak while E2 and W2 are thecentroid and the width of the second peakous chapter 4 is considered as if it were only related to the coulomb excitation.
In 70 Ni data analysis GDR excitation and decay were obtained in the same way describedin 5.3. In the left panel of fig. 5.13 the obtained excitation probability is plotted.
This spectrum was used as input in GEMINI++ code. The expected γ decay spectrum isdisplayed in right panel of fig. 5.13 (also in this case the RIPL-3 parameters were used).
As in the data analysis of Iron isotopes the GEMINI output was folded with the detector
Response Function.
In this case it was obtained with the SUNFLOWER simulation code (see appendix B),
and the efficiency obtained was compared with the one published in literature [58], [97],showing a good agreement.

Figure 5.13: Left panel: the excitation spetrum obtained considering a lorentzian shape GDR with
RIPL-3 parameters [87]. Right panel: the GDR γ decay obtained with GEMINI++ after the folding
with the response function.

The left panel of Fig. 5.14 shows a comparison between the experimental spectrum
and the tail of the GDR γ yield, while right panel shows the subracted spectrum. It
is possible to see that an unresolved structure is present between 5 MeV and the one
particle threshold energy.

5.5 E1 investigation in 70 Ni isotope

108

Figure 5.14: Left panel: the comparison between the GDR γ-yield (red band) and the experimental
spectrum. Right panel: the subtracted experimental spectrum.

The multipolarity of this high energy γ transitions was investigated using both LaBr3 :Cedetectors and DALI2 array. The ratio between the statistics collected for the 2+ level decay and this high energy yield was evaluated at different angles and compared with theone expected using the DWEIKO code as in the Iron case [93]. Here, thanks to the higher
statistics, the emission at different angles was evaluated and it is of E1 nature.
The fig. 5.15 shows this comparison: the experimental points reproduce quite well the
expected trend.

Figure 5.15: Comparison between the expected trend of the E2/E1 ratio (red line) and the ratio
between the statistics from 2+ level decay and the high energy γ-ray transitions (filled points).

Chapter 5: Discussion of experimental results

5.6

109

Final results

The B(E1) values related to the transitions in the energy range of 6-8 MeV were deduced
using the 62,64 Fe spectra shown in Fig.5.10 and the 70 Ni spectrum shown in fig.5.14.
The strength was deduced exploiting relation 5.7:
 c 2 v2 ξ2
32π 2 ZT2 α
2
2 2
ξK0 K1 −K1 − K0
σE1 =
B(E1)
9
~c
v
2c2
where K are modified bessel functions of the parameter ξ =(5.7)

ωf i bγv , E = ~ωf i is the excita-tion energy and b is the minimum distance, corresponding at minimum impact parameter at relativistic energies.
The converted B(E1) spectra, obtained using the scaling factors discussed in previous
sections and the 5.7 relation, are shown in Fig. 5.16 5.17 in the energy range 6 - 8 MeV.
We considered the summed B(E1) values in the range of 6-8 MeV for all the three nuclei

Figure 5.16: Left panel: B(E1) value spectrum in the range 6-8 MeV for 62 Fe. Right Panel: B(E1)value spectrum in the range 6-8 MeV for 64 Fe

and compared them with the same values already measured for other nuclei (as shownin fig. 5.18). The summed B(E1) values we obtained are here reported:
B6−8M eV (E1)=0.3 ± 0.1 e2 fm2 for 62 Fe
B6−8M eV (E1)=0.77 ± 0.27 e2 fm2 for 64 Fe
B6−8M eV (E1)=1.05 ± 0.28 e2 fm2 for 70 Ni
The plot in Fig. 5.18 shows that the values measured in this thesis are in the same rangeof the other nuclei already measured and reported in literature [28]. In addition the trendof the summed B(E1) as the N/Z ratio increases is confirmed, for the first time in literature, also in the case of exotic unstable nuclei.
In addition the Iron values were compared with the experimental results published5.6 Final results

110

Figure 5.17: B(E1) value spectrum in the range 6-8 MeV for 70 Ni

Figure 5.18: Summed B(E1) values in the range 6-8 MeV for nuclei already investigated in literature [28] and the results here obtainedin [92] for stable Iron (56 Fe). In this paper the total B(E1) in the energy region aroundthe one particle separation energy was investigated. Here a B(E1) value integrated on
the range 5-10 MeV was reported. The upper limit of this E1 strength amounted at 0.127
e2 fm2 . This value seems to indicate that the increase of the neutron number in Iron nuclei induces an enhancement of the dipole strength around the one particle separationenergy.
As regarding the Nickel value, the error bar is quite large in spite of the high statistics.

Chapter 5: Discussion of experimental results

111This is not only due to the experimental uncertainties but also to the nuclear interaction
contribution that may account up to 20% of the yield [96]. Even if the isoscalar excitation
is not predominant, it should be taken into account: as a consequence there are large
error bars.
The E1 response of the isotopes, here investigated, was also compared with the total E1
strength.The relation 5.8 explained in [7], was used to evaluate the total isovector electric
dipole EWSR.
Σn (En − E0 )B(E1, 0 → n) = 14.8

NZ 2
e f m2 M eV
A

(5.8)

Using the result of this relation, the percentage of the ESWR satisfied by the states here
discussed was evaluated. Here the results are listed:62

Fe : 0.9% ± 0.3 %64

Fe : 2.3% ± 0.78 %70

Ni : 2.7% ± 0.73 %Though the error bars are quite large, due to the low statistics collected in two shortbeam time, the percentage of the EWSR related to these states is not negligible and thetrend is clearly visible.

Conclusions and outlook

In this work the E1 response of 62,64 Fe and 70 Ni around the one particle separation energy was investigated. Coulomb excitation at relativistic beam energy was exploited toaccess the E1 strength in these neutron rich exotic nuclei. As introduced in this thesis,
the E1 response of nuclei around one particle separation energy attracted a lot of interest
due to its relation with nuclear structure and astrophysics aspects. The accumulationsof E1 strength in this energy region are commonly called Pygmy Dipole Resonance, incomparison with Giant Dipole Resonance that exhausts the major part of the isovector
dipole EWSR [7]. Theoretical interpretation of this nuclear feature is still under debate,but it was shown in literature that its strength is connected with the simmetry energy
term of nuclear Equation of State and the neutron skin thickness [2]. In addition it was
shown that this strength is relevant also for astrophysical aspects like neutron star structure and neutron capture reactions rate in exotic environment like supernovae [3].
In spite of the large amount of data available for stable nuclei, data about exotic nuclei
are still scarce. The relativistic coulomb excitation technique applied for the measurements here discussed, and explained in detail in this PhD thesis, allows together withpowerfull accellerators and modern detector systems to investigate also nuclei far fromthe valley of stability. The subject of this work is the investigation of E1 strength in neutron rich exotic nuclei using the state of the art detector arrays (AGATA,HECTOR+ andDALI2). In fact thanks to the connection of these structures with the neutron number
and in particular with the neutrons in outern shells, an enhancement of this feature is
expected for very neutron rich nuclei.
The experiments here discussed were performed in GSI and Riken laboratory. 62,64 Fe
113

114

Conclusions and outlook

were investigated during the PreSPEC-AGATA campaign in GSI, the experiment started
in the 2012 and it was concluded in the 2014; as regarding 70 Ni, it was measured in
Riken during the DALI2 campaign in the autumn 2014. In both cases the radioactive
beams were brought to collide with high Z value thick target to induce Coulomb excitation. The setup allowed to identify incident ions, the products of the reaction, to selectthe coulomb excitation reaction channel and to measure the γ decay of the de-excitationof the PDR in coincidence with the identified ion of the beam.
The γ-ray energy spectra showed an amount of statistics above the tail of Giant Dipole
Resonance around the one particle separation energy. As the measured transitions are
below the one particle separation energy, the good energy resolution of AGATA array
could be exploited.
The increase of statistics was evaluated in the energy range 6-8 MeV for all the threeisotopes. Fig. 5.19 and 5.20 show the final measured spectra.
We considered the summed B(E1) values in the range of 6-8 MeV for all the three nu-

Figure 5.19: Left panel: B(E1) value spectrum in the range 6-8 MeV for 62 Fe. Right Panel: B(E1)value spectrum in the range 6-8 MeV for 64 Fe

clei and compared them with the same values already measured [28] for other nuclei (asshown in fig. 5.21).
B6−8M eV (E1)=0.77 ± 0.27 e2 fm2 for 64 Fe
B6−8M eV (E1)=0.3 ± 0.1 e2 fm2 for 62 Fe
B6−8M eV (E1)=1 ± 0.23 e2 fm2 for 70 Ni
It is important to underline that the value here obtained are in the same range of the ones
already published. In addition, these results confirm the increase of the B(E1) strengthwith the N/Z ratio, observed for the stable nuclei. This trend is particularly evident in
the Iron isotopes: the two neutrons in 64 Fe seems to be responsable of a strong increasing

Conclusions and outlook

115

Figure 5.20: B(E1) value spectrum in the range 6-8 MeV for 70 Ni

Figure 5.21: Summed B(E1) values in the range 6-8 MeV for nuclei already investigated in literature [28] and the results here obtainedof the dipole strength. This confirmation is very important because, for the first time inliterature, it was verified in exotic nuclei far from the stability.
These results, in particular the ones about Iron isotopes, will be soon submitted for publication. The data about 70 Ni will be further analyzed also to investigate the strength
above the neutron threshold. The coming upgrades of the experimental facilities willallow to produce exotic nuclei with higher and higher intensity and therefore explore
more extreme neutron rich nuclei. The informations about the isovector character of116Conclusions and outlook

these states in the pygmy region, published in this thesis and the ones that will be provided in the next publications on the basis of this and a further anlysis, will provide
indications and references to new experiments for a more detailed investigation of thisstructures and also in more exotic nuclei.

A PPENDIX A

Statistical decay in the GEMINI++ code

In this Appendix, the GEMINI++ code will be discussed. The code was used in the data
analysis to have an evaluation of the γ yield of GDR decay. GEMINI++ is a statisticalmodel code written to predict complex fragment emission in fusion reactions. In particular, for a given excitation energy of the Compound Nucleus, the code follows the decay
using a Monte Carlo approach. This code is useful to have an estimation of the γ yieldfrom statistical decay; in addition it can be exploited to investigate how this yield change
as the varying of the gates on reaction products.

A.1

The code

GEMINI++ is a C++ code developed to investigate fusion-evaporation reactions. It was
written and developed by R. Charity [86], while GDR γ decay was implemented by M.
Ciemala [85]. The Hauser-Feshbach theory is the thoretical basis of the code. It is exploited to estimate fusion reaction cross sections and also to evaluate the particle emission in the evaporation stage. The code can be used to simulate a fusion evaporation
reaction or just to investigate the statistical decay of an excitated compound nucleus. In
this appendix the latter way of using the code is discussed because it was applied in
the data analysis here presented. The decay of the Compound Nucleus is treated witha Monte Carlo routine. The input required by the code consists in the excitation energy,
the spin and the diffusness parameter. The decay is processed as a series of sequential
binary decay. This iterative routine stops when the energy still avaible is too low to continue the decay cascade or the competitive γ decay prevails. The code considers only E1,
E2, M1 and M2 γ decay. As regarding dipole transitions, the Giant Dipole Resonance isalready implemented in the code.
117A.2 The statistical model

118

A.2

The statistical model

As already said in the previous section, GEMINI++ is based on the Hauser-Feshbachtheory. According to this formalism, the partial decay width of a Compound Nucleus
with a spin JCN and excitation energy E*, for the evaporation of a particle i is equal to:1
Γi (E∗, JCN ) =2πρCN (E∗, JCN )

∞
X

Z
d

JCN
+Jd
X

Jd =0 J=|JCN −Jd |

J+S
Xi

×

Tl ()ρd (E ∗ −Bi − , Jd )l=|J−Si |(A.2.1)
where T is the particle trasmission coefficient, ρ is the level density, while B and  areparticle binding energy and its kinetic energy. The evaporation channels here included
are: n,p,d,t,3 He,α,6 He, 6−8 Li fragments. The γ decay is treated separately. In this calculation [98] the separation energy, nuclear masses and shell corrections are obtained fromthe tabulations of Moller et al. [99]. Concerning transmission coefficients, the evaporation formalism is based on the condition of the detailed balance: this means that the barrier penetration is expected to be the same of the inverse reaction (absorption process).
The real optical-model potentials are used here [98], with the incoming-wave boundarycondition model (IWBC), to calculate transmission coefficients. The compound nucleus
thermal shape fluctuations and the fluctuations in the diffusness of the nuclear surface
originate a distribution of the Coulomb barriers. For this reason GEMINI [98] considers
an average of the transmission coefficients evaluated varying the radius for the nuclear
potential around the value obtained from the global optical-model fits.
A.2.1

The level density

The level density used in the code is obtained by the Fermi Gas formula, including several corrections. It can be written as:
ρ(E∗) = Kcoll (E∗)ρF G (E∗)

(A.2.2)where Kcoll (E∗) is a factor that include the enhancement of the level density above thesingle particle value, this is caused by the rise of rotational and vibrational bands due tocollective motions. The ρF G (E∗) is the Fermi Gas formula.
ρF G (E∗, J) =(2J + 1)√
exp(S)
24 2a1/4 U 5/4 σ 3(A.2.3)√where S = 2 aU , a is the level density parameter (obtained from single particle level
density), U is the internal energy while σ 2 = Irig T with Irig the moment of inertia andAppendix A: Statistical decay in the GEMINI++ code

119

T nuclear temperature. The a parameter is affected by shell effects; this was treated by
Ignatyuk et al. [100], and it was included in the parameter as follows:δWa(U ) = ea(U ) 1 + h(U )U(A.2.4)

where h(U ) = 1 − exp(η1 U ) with 1/η1 = 18.5 MeV. The ea(U ) has dependances frominternal energy and mass of the nucleus, GEMINI uses the following relation to take
into account these dependances:ea(U ) =A
k∞ − (k∞ − k0 )exp − k∞k−k0 U
A(A.2.5)where k is a function of mass: k(A) = 0.00517exp(0.0345A). k0 and k∞ are parameters
setted as k0 = 7.3 and k∞ = 12M eV . In this way for U=0 the dependence of ea by thenuclear mass is A/7.3, reproducing the fit of the experimental data as shown in fig. A.1.

Figure A.1: Mass dependance of level density parameter at temperature T=0. The filled points
are experimental results from neutron resonance measurements, the empty points are results from
calculations using Ignatyuk approach

A.2.2

The γ decay

GEMINI evaluates the γ decay probability using the standard definition of multipole
decay width (Blatt and Weisskopf 1958):Γγ )(Eγ ) =ρ2 X
ξl fl (Eγ )dEγ
ρ1l

(A.2.6)

A.2 The statistical model120(2l+1)

with fl (Eγ ) = Eγ

and ξl is the strength function. As regards the Giant Dipole Reso-nance, it is implemented by using a lorentzian type resonance shape. In particular threelorentzian compenents can be treated by the code. It is defined by the relation:3

σ = 2.09 × 10−5Z(A − Z) XA
k=1

Sk Eγ2 ΓGDR,k
22Eγ2 − EGDR,k+ Eγ2 Γ2GDR,k(A.2.7)

where EGDR,k are GDR component energies, ΓGDR,k the corresponding widths and Sk
the intensities. The GDR decay width is then defined as:2
ΓE1
γ = σEγρ(E ∗ −Eγ )ρ(E∗)(A.2.8)where ρ is the level density evaluated after and before the γ emission. The parameters of
GDR can be inserted as input or they can be computed by the code using the systematics
and refined with χ2 minimization. Also M1 and M2 gamma decay are considered in thecode. The decay width is obtained by:l2(l−1)/3 2(l+1)ΓMEγγ = Wul Ft D0 A

ρ(E ∗ −Eγ )ρ(E∗)(A.2.9)where Wu1 = 2.1×10−8 and Wu2 = 1.5×10−14 , D0 = 1 MeV and Ft is a correction factor
for the Weisskopf formula.

A PPENDIX B

The setup simulation code

In this appendix the AGATA simulation code is presented [40]. It was used in the data
analysis to build the Response Function. It is a Monte Carlo code developed in C++
programming language: it is diveded in several steps to simulate the reaction of theexperiment, the background, the γ detection and reconstruction. It was developed andtuned for PreSPEC setup in GSI loboratory.
In addition the HECTOR-DALI simulation code is presented. The core of the code is thesame of the one used for AGATA and developed for Riken setup.

B.1

The AGATA code structure

The AGATA simulation program is a C++ object oriented code. It accepts as input theparameters of the beam, the target and the γ decay scheme of the excited nuclei.
The geometry of AGATA array has to be implemented through configuration files.
The code simulates the reactions in the target, the background and the γ interaction
mechanism. The simulations are performed with the Monte Carlo approach. The codeuses GEANT4 libraries for the radiation-matter interaction. The results are organized in
ROOT files.
The simulation is divided in three steps: the Event-Generator, where the reactions that
emit γs are computed; the Event-Builder, where the γ detection of the experimental setup
is simulated; the Event-Reconstructor, where the analysis and γ-ray tracking are performed.
This structure is the same of the simulator code for the DALI setup in RIKEN. The codes
are very similar and both of them were used during the data analysis: one for GSI experiments, one for RIKEN measurement.
121B.1 The AGATA code structure

122

B.1.1

Event Generator

The event generator is the first step of the simulation. Here the interaction between the
beam and the projectile is considered. The input parameter files require information on:• BEAM: the mass, the charge, the kinetik energy of projectiles are required. In addition also the beam spot position on the target, the width and the angle between
the beam direction and the target are needed.
• TARGET: the mass, the charge and the thickness of the target are needed. In addition a table of the loss of energy per unit of length at kinetik energy varying isrequired. This table has to be specific for the beam-target coupling.
• γ DECAY-SCHEME: the γ decay scheme with the energy of the levels and the probability of the transitions has to be inserted as input. These informations about thenuclues of interest are listed in a separate parameter file.
The event generation step define also the total number of events that will be simulated.
In addition the atomic backround is computed at this stage.
B.1.2

Event Builder

The Event Builder stage consists essentially in the old AGATA simulation code developed by E. Farnea et al. for the AGATA campaign in Legnaro INFN laboratory [38].
The geometry of the AGATA clusters are implemented (both the triple and the double
clusters) [40]. The code require also the geometry of the target and the frame.
Monte Carlo routines are used to simulate energy release of γ-s and every interaction
point is characterized by a position, the amount of energy released, the timing information, the detector and the segment in which it occurs.
The interaction mechanisms here considered are: Compton scattering, photoelectric absorption, pair production, Rayleigh scattering.
B.1.3

Event Reconstructor

The last step of the simulation is the reconstruction of the events. Here the doppler
correction is performed on the basis of the informations coming from the previous steps.
In addition also γ filters can be applied: the MGT-γ ray tracking can be performed, or
also other γ-ray tracking algorithms.

Appendix B: The setup simulation code

123

Figure B.1: Left panel: AGATA simulated spectrum a 7 MeV γ ray emitted by a source in flightmoving with the same β of the experiment. Right panel: AGATA simulated spectrum a 7 MeV γ
ray emitted by a source at rest.

B.2

Simulations for 64,62 Fe experiment

The AGATA simulation code was used to obtain the Response Function of AGATA arrayfor the measurement. In particular the response function for both the in-flight and target
emission was computed. All the energy range from 0.5 to 18 MeV was scanned. The
efficiency obtained with the simulation was compared with both the one obtained fromthe 60 Co calibration run before the production runs and the one tabulated in technicalreports [75]. This was an important tuning to make the simulated setup as much as
possible similar to the laboratory setup. In addition it was verified that the simulated
efficiency, as a function of the energy, follows the expected exponential trend.
In fig. B.1 a comparison for the spectrum obtained considering a γ-ray at 7 MeV ofenergy emitted in-flight and at rest is shown. The spectrum obtained for the emission atrest is characterized by an higher energy resolution, due to the absence of the doppler
broadening. On the other hand the doppler boost enhance the absolute efficiency of theapparatus in the case of the in-flight emission.
The response function was used to evaluate the influence of the γ yield from GDR
decay in the AGATA spectra. In Fig. B.2 an example of the transformation appliedby the Response Function is shown. In addition the AGATA simulations were used toevaluate the efficiency in the energy range investigated in this thesis.

B.3

The HECTOR-DALI code

The simulation code developed for AGATA was adapted for the Riken setup by P. Doornenbal et al. [101]. The structure of the three steps: Event Generator, Event Builder and124

B.3 The HECTOR-DALI code

Figure B.2: Left panel: a lorentzian shape peak at 11 MeV, used as input of the AGATA Response
Function. Right panel; energy spectrum output of the Response Function

Event Reconstructor was maintained. The code allowed to simulate both DALI, already
implemented, and HECTOR setup, implemented for the 2014 campaign. The code, as
in the case of AGATA, was used to compute the response function for the two apparata. The efficiency from the response function for the LaBr3 :Ce detectors was comparedwith [58] to check that the code provide a good estimation of the efficiency. In fig. B.3
the efficiency of the HECTOR array for γs emitted in flight is plotted as function of theenergy.

Figure B.3: Simulated absolute detection efficiency for γs emitted in-flight. It was obtained with
the HECTOR response function in Riken (an interval of 1 MeV was considered).

A PPENDIX C

Femul and prespec data analysis codes

In this appendix a short description of the codes used for sorting the raw data collectedin the experiments in GSI is presented.
The informations here reported are based on the tutorials and presentations at the data
analysis workshops held by the developers of these codes. This is not a full explanation
or a manual for the users of the codes. The aim is providing an overview of the logic at
the basis of the tools used for this complex data analysis.

C.1

Femul

Femul [102] is an emulator of the NARVAL system [70] used for the AGATA data handling. It was born with the aim of helping the debugging of NARVAL system but it is
now one of the most used approach to sort AGATA data offline. It can be considered afull emulation of the NARVAL framework with the exception that it is a simple process
running on a specific server, while NARVAL involves more computers.
As introduced in chapter 3 the algorithm follows a rigid data-flow where every step iscalled ”actor”. The configuration for the crystals and the data flow is defined in the socalled ”topology” files. Every actor has specific configuration files.
The data flow can be divided in two parts: a local process, where the data of every detector are separately processed and a global process where the data from every crystal
are merged between them and with the ancillary detectors, in the end the tracking algorithms are applied.
In this data analysis, only the local part of the data flow was processed: the merging of
the data and the event bulinding were performed using the prespc code. The tracking
algorithm was tuned to have the best performances, for this reason it was necessary to
125

126

C.1 Femulchange the settings of this library respect to the one provided by the prespec package.
The AGATA raw data are written in separated files for every crystal. For this reasonfrom the very beginning the first part of the Femul data flow runs the data from every
detector in an indipendent way from the others.
The first actor is the Crystal Producer: it reads the data and prepares them in a frame to beprocessed by the next actors. In particular it acts as a local event builder: the data fromevery mezzanine is organized as a part of the data from the same crystal.
The next actor is the Preprocessing Filter: it applies calibrations and a first filtering of thesignal. Cross talk corrections are applied at this stage, in addition the net-charge segments are identified.
The most significant actor in this local process is the PSA Filter: it applies a GRID searchalgorithm to extract the position of the interaction in the segments. The algorithm is a
simple comparison between the digitized and recorded signal and a set of signal samples
called AGATA signal basis. This set of samples is obtained by accurate measurements
and calculations of the electric field in the detector. The algorithm simply compares the
samples with the signal recorded and chooses the one that best fit the data. In Fig. C.1
an example of a superposition of the signal measured and the sample chosen by thealgorthm is shown. The selection of the samples allows to obtain the position of the interactions. In fact every samp,e is associated to a specific γ interaction position.
A last actor was inserted at the beginning of the GSI experimental campaign of AGATA:
the Post-PSA Filter. It applies neutron damage corrections and further calibrations that
re-correct the one applied at preprocessing level. In this analysis this step was not considered because the prespec code requires AGATA data as output of PSA filter.
The AGATA data are written in ADF files (AGATA Data Format) and they can be used
as input of other analysis codes like prespec or Go4 [104].
The global part of the data-flow is composed by Event Builder - Event Merger actors andthe tracking filter. In this part of the data flow the data from different crystals are used tobuild an ”event” considering the timestamp, the same logic is used by the Event Merger
to build the global event using the AGATA event and the data from ancillary detectors.
The last actor is the Tracking Filter: it applies tracking algorithm using MGT libraries.
This class of procedures applies the γ-ray tracking selections on the basis of the considerations explained in chapter 3. The code clusterizes the γ interactions, provided by
PSA, and it finds the best combination of them minimizing the χ2 . It is an important
aspect choosing the threshold of acceptance of this figure of merit on the basis of the
background level that affected the measurement.

Appendix C: Femul and prespec data analysis codes

127

Figure C.1: Superposition of the signal recorded (red line) and the sample chosen by the algorithm(white line). The last signal is from the central core contact.

In spite of previous actors, the output of this last one is a ROOT file where all the informations extracted by the raw data are organized in a Tree.

C.2

prespec

The prespec code [103] was developed for the online-acquisition and the data analysis
for the AGATA experimental campaign in GSI with the PreSPEC setup. It is a C++ codethat can be considered an upgrade of the previous version of the offline Go4 data analysis code. It was released in 2014 for the last part of the experimental campaign. In thisfirst release the data of AGATA and MBS are merged and processed.
The code accepts data merged online in lmd format, where lmd is the List Mode Data
format in which MBS data are usually recorded. Another working available mode accepts as input the AGATA data from PSA Filter and the lmd files from MBS.
Prespec code, like Femul, merges the data from the two systems: NARVAL and MBS. On
the basis of the timestamp the coincidence is checked and the merging performed: forthis reason a particular care is required that the input file are in the correct time-order,
otherwise the coincidence could be lost and the events are not built.

128

C.2 prespec

After the merging, the analysis can start.
The first step of the data flow is performed by the so-called ”crates”. Every detector system has its own crates that call the correct unpackers for reading and preparing the data
for the next analysis stage. In the code the every unpacker is identified as a particular”module” of a defined ”crate”.
The next step of the analysis is performed the ”processors”. Every processor calls as
input the data from the unpacker or from another processor. The processors apply calibrations and filters on the data. Every detector system has a set of processor.
This overview of the prespec code shows that also in this case, as in Femul, the data flow
is quite rigid: the direction of the processing cannot follow loops or conditional calls of
the processors.
The data analysis code is built in a way that it keeps all the libraries with the codes in afolder. The user can organize the data analysis of the raw data defining for every detector apparatus a set of configuration files that provides: calibration parameters, gates forfiltering, the set and the order of the procedures to call to unpack, calibrate and filter thedata.
The output of this code is a ROOT file where the processed data are organized in a Tree.
The user can choose how to build this tree selecting the processors of the detector systems of interest.

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Acknowledgments

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