# Presentation: 464327

## The ICHOR project : spin-isospin response study (for 2ν2β decay) 	and magnetic spectrometer SHARAQ

- H. Sakai
- University of Tokyo

- The third LACM-EFES-JUSTIPEN
- Workshop at Oak Ridge

- February 23-25, 2009

## What is the ICHOR project ?

** “****I****sospin-spin responses in ****CH****arge-exchange**** ****ex****O****thermic**** ****Reactions”**
** ****( Grant-in-Aid of MEXT )**

**1. Study of the intermediate nuclear structure for ****2ν2β decay **** **
**	**** ****‧****48Ca(p,n)48Sc and 48Ti(n,p)48Sc  reactions at 300 MeV**
**2. The magnetic spectrometer SHARAQ construction at RIBF in RIKEN**
**	****‧ ****present status **

**Based on the works by**
**K. Yako (****for 2****ν2β ****decay)**
**SHARAQ collaboration**

## Study of intermediate nuclear structure of 48Sc for 48Ca 2ν2β decay via. (p,n) and (n,p) reactions at 300 MeV

**Study of intermediate nuclear structure of ****48****Sc for ****48****Ca 2ν2β decay via. (p,n) and (n,p) reactions at 300 MeV**

**Courtesy by K. Yako**

## Two-neutrino double beta decay

- Half lives ... not understood well

- Half-life and matrix element:

- (A,Z)

- (A,Z+1)

- daughter

- (A,Z+2)

- 2νββ decay

-  second order weak process.
-  rarest process confirmed so far.
-  2νββ is very useful to test theoretical models.
-   Same models are used for 0νββ analysis.

- intermediate

| Nucleus | Exp T1/2   (y) | Calc T1/2     (y) |
| --- | --- | --- |
| 48Ca | ~ 4.3 x 1019 | (1.3 – 6.0) x 1019 |
| 76Ge | ~ 1.4 x 1021 | (0.8 – 1.4) x 1021 |
| 82Se | ~ 0.9 x 1020 | (0.1 – 1.1) x 1020 |
| 96Zr | ~ 2.1 x 1019 | (3.0 – 11) x 1019 |
| 100Mo | ~ 8.0 x 1018 | (1.7 – 32) x 1018 |
| 116Cd | ~ 3.3 x 1019 | (5.1 – 10) x 1019 |
| 128Te | ~ 2.5 x 1024 | (0.6 – 37) x 1024 |
| 130Te | ~ 0.9 x 1021 | (0.3 – 2.7) x 1021 |
| 150Nd | ~ 7.0 x 1018 | (6.7 – 27) x 1018 |

- Suhonen  et  al., PR300(1998)123

- parent

**T****1/2 ****is not enough to test theories.**

**Notes:**
2’20
Two-neutrino double beta decay ... is a second order weak process and we can say that it is the rarest process confirmed so far in nature.
If it is thoroughly understood, it helps the analysis of zero-neutrino double beta decay rate, which is related to the Majorana neutrino mass.

The half life is connected to the nuclear matrix element through the factor of weak coupling and phase space,
and the matrix element consists of energy denominator and product of the GT matrix element; from the parent to intermediate nucleus and from the intermediate to daughter nucleus.

This table shows how well the structure theories were doing in 1998.
I picked up the numbers from the review paper by Suhonen. 
There should be some progress since then, but the half life is not theoretically well understood.
So experimental studies of GT strength distributions are useful to help the understanding of the matrix element since the GT strength give you the matrix element except its sign.

## B(GT) in low-lying states of 48Sc

- B(GT) in low-lying states of 48Sc

- Low lying states
- ... high resolution measurements

**GT strengths: ****← **charge exchange reactions at intermediate energies

- Grewe et al., PRC76(2007)054307

- 48Ca(3He,t) @ 140A MeV (RCNP)
- 48Ti(d,2He) @  90A MeV (KVI)

- 48Ca

- 48Sc

- 48Ti

- = 4276 keV

- (p,n) type

- (n,p)  type

**(****3****He,t)**

**(d,****2****He)**

**Notes:**
1’10
Here is a famous example of such a study on 48Ca, discussed by previous speakers.  
The contribution of low lying 1+ states were studied by high-resolution measurements of both (3He,t) and (d,2He) reactions and a state-to-state correspondence was obtained. 
Then, the contribution of each state was discussed from the strengths.
They have succeeded in reproducing the half life by the states below 5 MeV excitation..

(In other words, the contribution from the states above 5 MeV cancels out when summed up.) 

## “Contribution” of low-lying states 

- “Contribution” of low-lying states

- No sign info, always additive sum
-       → upper limit

- Grewe et al., PRC76(2007)054307

- Decay measurement :

- matrix element “w/o sign” :

- Are these B(GT) distributions good enough to test nuclear structure models?
-  ..., Of course NOT.

- NEMO3 (preliminary)

- 	(4.4        ±0.4) x 1019  y

- +0.5
- - 0.4

- M2v→ 0.045 MeV-1

## Shell model calculation 

- Same as Horoi et al.
- PRC75(2007)034303

- “w/o sign”

-  GXPF1A
-  QF = 0.6

- Shell model
- (full fp)

- Reproduce low energy part rather well!

- Shell model calculation

- Only 5% of total B(GT-)!

- GT GR

## Aim

- Measure full profile of the B(GT) distribution to test /constrain  theoretical models.
- Measurement
-  B(GT+/-) distributions
- Ebeam= 300 MeV
- θ = 0°~12°

- 48Ca

- 48Sc

- 48Ti

- (p,n)

- (n,p)

- GTGR

- 48Ca(p,n)48Sc
- 48Ti(n,p)48Sc

- 116Cd(p,n)116In
- 116Sn(n,p)116In

- ?

**Notes:**
0’30-
If your strategy is to check or constrain the calculations by data, you need the full snapshots of B(GT) distribution.
So we started the study of the GT states up to the continuum, by the (p,n) and (n,p) reactions at 300 MeV.

## (p,n) & (n,p) facilities at RCNP

- 100 m TOF tunnel

- LAS

-  2x106 neutrons/s
-    by 7Li(p,n)

**Notes:**
0’30-
The measurements were performed at RCNP Osaka.
It has a 100-m Time of flight tunnel and there is a set of neutron counters. 
The (n,p) facility is located at the west experimental hall, and it utilizes the large acceptance spectrometer.

## Measurement and results on

**Measurement and results on**
**48****Ca(p,n)****48****Sc and ****48****Ti(n,p)****48****Sc  reactions**
**at 300 MeV **

## 48Ca(p,n) measurement

- 48Ca(p,n) measurement

-  48Ca target
-   17 mg/cm2, 98%
-  energy resolution
-    410 keV
-  angular range
-    0 – 41 deg

**Notes:**
0‘30
In the (p,n) measurement, proton beam hit the target and the scattered neutrons were detected by NPOL3 neutron counter.
The energy resolution is 400 keV.
We took the cross section spectra from 0 degrees to 40 degrees.

## 48Ti(n,p) spectra

- 0 -12 deg
-  energy resolution
- 1.2 MeV
-  statistical accuracy
- 1--3% / 2MeV・1deg
-  systematic uncertainty
- 4%

- 48Ti(n,p) spectra

**3 x 300 mg/cm2, 2 x 3 cm2**
**(****c.f.  Alford et al.: 130mg/cm2****)**

**Notes:**
0’40
This is our dataset of (n,p) measurement.
The angular range of 0 to 12 degrees were covered by three angular settings of LAS.
At 0 degrees, you can see two GT peaks at 3 MeV and 6 MeV, and the strengths decrease with angle.
We performed a Multipole decomposition analysis to extract the GT strength distribution. 

## Multipole decomposition analysis

-        t-matrix by Franey & Love @325 MeV
-  optical model parameters:
-        Global optical potential
-        (phenomenological, Cooper et al.)
-  one-body transition density:
-        pure 1p-1h configurations
-        radial wave functions  ... W.S. / H.O.

- Particle: 	1f, 2p, 1g, 2d, 3s, 1h11/2
- Hole:		1p, 1d, 2s, 1f

- 48Ti(n,p) angular dist.
- Ex = 15 MeV

- MDA

- DWIA

- DWIA inputs

**Notes:**
1’00-
In multipole decomposition analysis, the experimentally obtained cross section data at each energy bin
are fitted by calculated angular distributions.
We put these 7 Jpi transitions. 
The angular distributions are shown here.
The GT components have peak at 0 degrees, the dipole, 3-8 degrees and the quadrupole around 8-11 degrees.
The inputs of the DWIA calculations are effective interaction, optical model parameters, and the one-body transition density. 
We used these pure or simplest 1p-1h configurations, which cover most of the strength.

## Reliability of angular distribution

- The ΔL>4 component does not contribute much at 0°

- The description of  ΔL=2 is reasonable.

- The DWIA description of  GT transition is good.

**Using only ****Δ****L=0,1,2,3 seem to be justified.     **

## Decomposed spectra

- Sasano/Miki

**Notes:**
0’30-
The decomposed spectra look like this.
The (p,n) 0-degree spectrum is almost entirely due to the deltaL=0 component. 
The (n,p) spectrum also contains some small monopole contribution in the continuum. 
At 5 degrees spin dipole resonance is seen in both spectra. 
%Please note that the vertical scale is enlarged for the (n,p) spectra. 

## Proportionality relation

- kinematical correction
- by DWIA

- GT unit cross section

- A-dependence of
- (p,n) @ 300 MeV

- Sasano

**Deducing B(GT) using proportionality relation**

**Same****  ****       ****  used for both (p,n) and (n,p).**

**Notes:**
0‘50
(before) The GT strengths are obtained by using the proportionality relation.
The monopole cross section is related to the B(GT) through the GT unit cross section. 
It is estimated to be 3.2 mb/sr from the mass number dependence.
The B(GT) value for the (p,n) transition going to the ground state of 116In is 0.26+/-0.02.

Our result is half of the result of the EC measurement.
We note that this decay measurement is difficult because of the small branching ratio of smaller than 0.1%.

## B(GT+/-) distribution

- MD analysis ...
- (p,n) : strength exists
-           beyond GTGR
- (n,p) : peak at 3 MeV
-           shoulder at 6 MeV
-           bump(?) at 12 MeV

- Integrated strengths

- (Ex < 30 MeV)

- Ex < 5 MeV ... consistent with
-                         (3He,t ) & (d,2He)

- New

- Contamination of IVSM?

- isovector spin monopole ...  ΔS=1, Δ L = 0,     2ħω, Op = r2στ

- contribution estimated by DWIA:   1.0 for (p,n), 0.9 for (n,p)

- ΣB(GT-) = 15.3±2.2
- ΣB(GT+) =  2.8±0.3

**Notes:**
0’30-
Let’s see both B(GT) spectra, from 48Ca to the intermediate 48Sc, and from the 48Ti to the 48Sc. 
Please note that the strengths are relatively weak in the B(GT+) side. 

...
この先(M2vの議論をする際には)、IVSM のことを忘れることにする。

## B(GT+/-) distribution ... comparison with shell model

- QF = 0.6

- Shell model ...
-       with quenched operator
- Spectra are well reproduced
- up to ...
- (p,n) : Ex = 15 MeV
- (n,p) :           8 MeV
- Strengths beyond
- ... underestimated.

-  larger model space?
-  deformation?

- (n,p) channel :
- ΣB(GT+;exp) = 1.9±0.3...
-      (w   subtraction of IVSM)
- ΣB(GT+;ShellModel) = 0.9

**Notes:**
0’30-
#Let’s see both B(GT) spectra, from 48Ca to the intermediate 48Sc, and from the 48Ti to the 48Sc. 
#Please note that the strengths are relatively weak in the B(GT+) side. 

The shell model calculation looks like this.

So maybe new things such as deformation or larger model space should be considered.
I hope we can hear some talks on this subject tomorrow.

I am an experimentalist and let me just demonstrate what happens with the unsigned nuclear matrix element.

#...independent particle model gives 4.1 (wo quenching).

#There are some sorts of correlation, such as BCS-type, short-range, tensor, ...
#I am not sure which is responsible, but at least one needs to extend the model space to account for the spin monopole component.

## Contribution to M2v

**matrix elements w/o sign:**

**At  8 MeV < E****x**** < 15 MeV**
**    ****dB(GT****-****)/dE : large**
**→ ****excess B(GT****+****) might have **
**     ****significant contribution on **
**     ****M****2v****.**

**Consequence of **
**(true) matrix element with sign **

**... ****unknown.**
**We must rely on theorists.**

**Notes:**
0’50
Let me just demonstrate how much the consequence might be on the nuclear matrix element.

Even though the energy denominator suppresses the contribution of the strengths in the high excitation energy region, there is a big difference between the data and the calculation. 

However, ,,

## QRPA prediction by Rodin (preliminary)

- QRPA
-      G-matrix + gpp
-      No quenching (QF = 1.0)

**Notes:**
It may be a good idea to use RPA to extend the model space.
Here is the QRPA prediction by Tuebingen group. 
I heard that QRPA is not good for 48Ca, but somewhat better for 48Ti. 
This calculation has the same problem of underestimation of beta+ strengths.

When the 2hw configurations are included, beta- spectrum looks almost intact.
However, the beta+ strength is increased.

When we put the transition density of 1+ into the reaction code, we obtain the spectrum like this.
To understand the high excitation energy region, one must take account of IVSM explicitly. 
And one can say that even without quenching, the monpole strength is underestimated.  

## Summary for 2ν2β decay

**       ****the ****48****Ca(p,n)****48****Sc / ****48****Ti(n,p)****48****Sc ****reaction**
**MD analysis  ****→ ****B(GT****+/-****)**** ****distribution (E****x**** < 30 MeV)**
**48****Ca → ****48****Sc → ****48****Ti**
**Σ****B(GT****-****) = 15.3±2.2        ****Σ****B(GT****+****) =  2.8±0.3**
** ****shell model predictions**** ****:**
**B(GT****-****): good agreement up to GTGR.**
**	****	****B(GT****+****): reasonable for E****x**** < 8 MeV, ****underestimate for E****x**** > 8 MeV.**
** ****QRPA by Rodin**
**	****	****B(GT+): IVSM is important?**
**M****2ν**** ****: large contribution from excited GT states.**
**Uncertainty remains due to the ****IVSM ****contribution.**
**      ******** ****to be explored by ****SHARAQ ****magnetic spectrometer **
**          ****under the ****ICHOR ****project.**

- Summary for 2ν2β decay

**Notes:**
1’20-
This is the summary.
We measured (p,n) and (n,p) reactions to study the B(GT) distributions in the intermediate nuclei of double beta decay.
By using MD analysis, we obtained the B(GT) distributions. 

For the Ca case, we obtained a new bump at 6 MeV in B(GT+) spectrum and some extra strengths above 15 MeV excitation.
The B(GT-) distribution is in good agreement with the shell model up to the giant resonance region.
The B(GT+) distribution is fine up to 8 MeV, but the calculations underestimate the strengths above 8 MeV.

The data of 116Cd suggests similar problem in the B(GT+) side.  

I hope some theorists solve this problem of B(GT+) and solidify our understanding of (2-nutrinino) nuclear matrix element.

Thank you.

## The magnetic spectrometer SHARAQ  at RIBF in RIKEN

**The magnetic spectrometer SHARAQ  at RIBF in RIKEN**

**what is new? : ****unstable nucleus as a probe**

**(under the ICHOR Project)**

## Spin-isospin responses and reaction kinematics

**Reaction kinematics dictates q and ****ω**** relation. **

**Interesting Spin-isospin responses often **
**     ****locate at ****q****~****small at high ****ω****. For example;**

**Double Gamow-Teller (DGT) resonance **
**Isovector Spin Monopole (IVSM)**** ****resonance **

**ω****>0 and *****q *****= 0 (time-like) can be reached by**
**     ****exothermic HICE reactions****.**** **

****** ****Stable nuclear beam excites only ****ω**** < *****q***** reagion **
**   ****(space-like)!  **

**Spin-isospin responses and reaction kinematics**

## New idea to use unstable nuclei 

- With stable beam
- With unstable beam

- ***m ***< 0: endothermic

***T******z***

- ***m ***>> 0
**EXOTHERMIC**

- ***m / *********

- RI beam is capable to probe the   q region.

- Photon Line

- Courtesy of Shimoura

## Example of exothermic CE reactions

**Example of exothermic CE reactions**

**Exothermic CE reactions: (****12****B,****12****C)/(****12****N,****12****C) **
**      ****Q=+13 MeV/ +17 MeV**
** ****Endothermic CE reactions : (****12****C,****12****N)/(****12****C,****12****B)**
**               ****Q=-17 MeV/ -13 MeV****	**

**Energy resolution for spectroscopy**
**	********E ****~****500keV  for A=12****、****E/A=300MeV particle**
**	****	****0.5MeV/(300×12)MeV = 1.3×10****-4**
**	****→**** ****corresponds to momentum resolution of**** p/********p ~15000**
**Angular resolution   ****⇔**** ****momentum transfer resolution**
**	****	****ex. ****12****N, 300MeV/A****	****	****9GeV/c**
**	****CRITERION:  *********q***** < 0.1 fm****-1 **
**	****	******************~ ****p(beam)×********q     ****→****  ******** ****< 2 mrad**
**	****	****	****	******** ****= 1 mrad**

**exothermic CE reaction achieves *****q*****=small ****with an excellent spin-isospin selection,****△****S=1, ****△****T=1**

**Intense unstable beams**
**               ****+**
**Dispersion matching BL**
**               ****+**
**Magnetic spectrometer**

## Let’s look at the magnetic spectrometer SHARAQ

**Let’s look at the magnetic spectrometer SHARAQ**

## What is SHARAQ? 

**SHARAQ is a ****high resolution ****magnetic spectrometer**
**      ****for unstable (secondary) beam experiments.**
**Installed at RIBF of RIKEN**
**	****	**

**      ****d,....,****238****U**** ****350MeV/****nucl.****   **
**       →**** ****RI beam by fragmentation**

**Expected intensity  (****14****N 250 MeV/A****)**
**    ****12****N: 1.6×10****5**** cps/pnA (max. 4×10****7 ****cps)**
**   ****12****B: 2.8×10****5**** cps/pnA (max. 7×10****7 ****cps) **

## SHARAQ  Characteristic

**SHARAQ  Characteristic**

**QQDQD type**
**Maximum rigidity 6.8 Tm**
** ********p/p = 14700**
**Dispersion matching  (x|********), (********|********)**
**Angular resolution < 1 mrad**
**Solid angle 2.7 msr / 4.8 msr**
**Rotatable (-2 to 15 degree)**
**Weight 500 tons**

- A/Z=3
- 220MeV/A

## Experimental room E20 @RIBF 
	14 July 2007 – 19 October 2007

**	****14 July 2007 – 19 October 2007**
**	****	**

- Documentary film of SHARAQ construction

## Present SHARAQ 

**Commissioning run starts March 23, 2009 !**

**First accepted experiment: search for IVSMR(*********** *****+****) by (t,****3****He) reaction**

##     IVSMR( -)  – some signatures observed

-  **Compression** **mode**

- L=0, S=1, T=1,  **2ħ******

_**experimental data**_
-     **IVSMR(*********** *****-****)  – some signatures observed**
**    ****IVSMR(*********** *****+****)  **–    **none**

- Courtesy by K. Miki

## Thank you for your attention.

**Thank you for your attention.**

## Backup 

**Backup **

## 116Cd(p,n) & 116Sn(n,p) results

- 116Cd(p,n) & 116Sn(n,p) results

- Sasano

- B(GT) distributions

- The ΔL=0 strengths seem to be underestimated (if QF~0.6).

**Notes:**
1’30-
Let me show you the result of 116Cd, only briefly. 
By the MD analysis, we obtained the B(GT) distribution for the (p,n) side and the (n,p) side.
#The vertical scale is ten times different. 

#The integrated strengths are 33 and 7 up to 20 MeV excitation, and it becomes 4 when the IVSM #contribution is estimated and subtracted (not the latest numbers).
A QRPA prediction by Alvarez-Rodriguez by deformed basis looks like this.
If the nuclei are deformed and the wave functions are adjusted to reproduce the B(E2) values, the B(GT) distributions change like this, pushing up the B(GT+) towards higher excitation energy.
On the other hand,  Sagawa-san sent us the RPA prediction of IVSM just after the experiment. 
It gives a reasonable description in the higher excitation energy region. 

Putting them together might account for the whole spectrum, but assuming no quenching in the 
Beta+ channel only is not reasonable.

## 48Ca(p,n): Other multipoles

- reliability

- good

- poor

- Excitation energy (MeV)

- Double differential
-  cross section (a.u.)

-  ΔL=0 component is the most stable.
-  ΔL>0 components suffer from node ambiguity. (0+2ħω, 1+3ħω)
-  Uncertainty due to the unbound final states.

- MDA by sasano

- Spectra

- Reliability

- One must be careful extracting ΔL>0 components in high Ex region.

**Notes:**
These figures show the spectra at angles where each multipole component is at the maximum contribution. 

If the main component of the giant resonance moves toward high excitation as the DL increases. 
...

## Concerns

- IVSM
- should be confirmed by “surface probes”:
- 		        measurement with heavy ion beams.
- Interference with GT?
- Uncertainty due to reaction mechanism in the continuum
- Transition density
- “Quasifree scattering” around 0 degrees

## (p,n) & (n,p) at 300 MeV

**Advantages**

-  **300 MeV****: **
** ****Distortion effects are smallest (   ).**
** ⇒ ****Analysis with DWIA is reliable.**
** ****SF/NSF is largest (         ).**
** ⇒  ****Transitions are mostly SF type.**** **
** ****Tensor interaction is smallest (    ).**
** ⇒ ****Proportionality relation is reliable.**

- tensor
- FraneyLove

** ****Most reliable multipole decomposition analysis (MDA) is possible.**

- cross section

- strength

**(p,n) & (n,p) at 300 MeV**

## Proportionality test by shell model

- Exercise by using:
-  48Ca--48Ti system
-  Shell model calc. (n ≤ 4)
-  Standard DWIA calc.

- Deviations are small
- for large B(GT)
- for both sides.

- 48Ca(p,n)48Sc

- 48Ti(n,p)48Sc

- unit cross section (A.U.)

- B(GT-)

- B(GT+)

- Sasano

- 1

- 0.01

**Notes:**
1’40-
Dr. Sasano made a shell model calculation in fp shell by using oxbash.
And he obtained unit cross section vs B(GT) for thousands of 1+ transitions for the (p,n) and (n,p) channels. 
The horizontal axis is in logarithmic scale. 

Certainly the unit cross section depends on the transition, but the deviations are small for transitions with large B(GT) for both sides.
Since experimental energy resolution is rather limited, spectra are smeared out so that the averaged unit cross section, indicated by the green line, might work.

Here are the expected spectra. 
The red curve shows the result of calculation with shell model transition density, and black curve is that by using the averaged unit cross section. 
The (p,n) spectrum is well reproduced by the unit cross section.
Since the B(GT) in the (n,p) channel is smaller the approximation is worse, but the difference here is at most 10% by virtue of our low energy resolution.  

## 116Cd(p,n) at 140 MeV vs. 116Cd(3He,t)

- 0°spectrum:

-  GT component: 0 MeV
-  Poor agreement with
- (3He,t) spectrum

- counts

- 116Cd(p,n) at 140 MeV vs. 116Cd(3He,t)

- Akimune et al. (1997)

- E293 (Sasano)

## Controversy with (3He,t) result(group)

**Controversy with (3He,t) result(group)**

| probe | B(GT; g.s.) | Ref. |
| --- | --- | --- |
| Electron capture |  0.47  ±0.13 | M. Bhattacharya et al., PRC 58 (1998) 1247. |
| (p,n) @ 35MeV |  0.16 | H. Orihara et al., NPA 577 (1994) 9. |
| (3He,t) @ 450 MeV |  0.032±0.005 | H. Akimune et al., PLB 394 (1997) 23. |
|  |  0.14±0.03 | H. Akimune et al., PLB (2008) Erratum |
| (p,n) @ 300 MeV |  0.26  ±0.02 | this work |

**Notes:**
1’30
Here is an example of such a study on 116Cd, using charge exchange reactions.
The contribution from low lying 1+ states can be studied by high resolution measurements such as (3He,t), and (d,2He) reactions.
These zero-degree spectra, taken from the paper by Rakers et al., may give you the idea of state-to-state correspondence.
The contribution of each state can be discussed from the B(GT) values of each transition.

However, I must say that we have to forget about this (3He,t) data by Akimune et al., due to the problem with isotopic purity of the target. 
A new (3He,t) measurement has been performed by Okamura-san et al. and the analysis is in progress.

## Contribution of g.s. in 116In to M2ν

-  B(GT-) = 0.26 ± 0.02  (This work)
-  B(GT+) = 0.256 ± 0.001 (β decay)

- 116Cd

- 116Sn

- intermediate

- 0+

- 0+

- 1+

- 1+

- g.s.

- 116In

- Transition through g.s. accounts for the half-life of 116Cd.

- Contribution of g.s.

- ⇒

- 2νββ decay measurement

- →

- ‘Single-state dominance’
- is not necessarily
- universal.

- running sum of M2ν(76Ge)

- Šimkovic et al., NPA733(2004)321

- M2ν(g.s.) = 0.070 ± 0.003 (MeV-1)

- M2ν(total) = 0.064 ± 0.007 (MeV-1)

## Nuclear matrix elememnt of 0νββ decay

- < 1995

- 1995 - 2000

- > 2000

- J. Suhonen, 2005

- Values from the
- Majorana Collaboration
- web site (2006)

- Courtesy of J.P. Schiffer

## (n,p) measurement

**(n,p) ****実験施設**

- (n,p) facility

-  2x106 neutrons/s
-    by 7Li(p,n)
-  angular range of
-   0-12deg is covered
-   by 3 angular setting
-   of LAS

**Notes:**
0’30
In the (n,p) measurement, the neutron beam is produced by the 7Li(p,n) reaction.
Then the neutron beam hits the (n,p) target in the wire chamber box. 
The momentum of the scattered proton is analyzed by the Large Acceptance Spectrometer. 

Since the beam is a secondary beam, we need a thick target to obtain a reasonable counting rate.

## 48Ti target

- 48Ti(n,p) at TRIUMF (1990, Alford et al.)
- metal 48Ti: thin ... low statistics
- Data at 3 angles
- ... not enough for MD analysis
- 48TiO2: contribution of oxygen
- at E*x  *> 6 MeV

- metallothermic reduction
- 		(IIS, Okabe Gr.)
- TiO2 + 2Ca = Ti + 2CaO
- 48TiO2 13g → 48Ti 5g (70%)
- purity:  98.7%
- 2. solidification by pressure
- 3 x 300 mg/cm2, 2 x 3 cm2
- (c.f.  Alford et al.: 130mg/cm2)

- Alford et al., NPA514(1990)49

**Notes:**
1’20-
There is a similar measurement at TRIUMF, and apparently they could not prepare a sufficient amount of the target material.
48Ti is usually provided as an oxide form. 
And they used thick oxide targets and a thin metallic foil.

Since the oxygen affects the spectrum above 6 MeV excitation it was difficult to obtain the B(GT) distribution in the continuum. 
On the other hand, the data from the metallic foil suffers from low statistics and data were taken only at 3 angles.
It is rather insufficient to detailed MD analysis.

So I asked this expert group for reduction of titanium dioxide.
Professor Okabe is in IIS, the institute of industrial science of  University of Tokyo. 
They succeeded in extracting the metallic powder from this small amount of titanium-dioxide by way of metallothermic reduction. 
And I used a press and obtained these thick Ti targets. 

## Decomposed angular distributions [48Ti(n,p)]

- Decomposed angular distributions [48Ti(n,p)]

- ΔL=0

- by Miki

- ΔL=1

- ΔL=2

- ΔL=3

- 1.0 MeV

- 9.0

- 3.0 MeV

- 11.0

- 17.0

- 19.0

- Double differential cross section
-  (mb / sr / MeV)

- Scattering angle (deg)

- 0       5      10

- 0       5      10

- 0       5      10

**Notes:**
0:30-
These are some examples of the decomposed angular distributions,
At 3 MeV, the experimental cross section has a peak at 0 degrees and it is due mostly to the GT component.
At larger excitation energies, the cross section has the maximum at finite angles but still contains some DeltaL=0 component. 

## 簡単な模型で

- 始状態

- 終状態

- 中間状態

- 始状態,終状態のどちらからでも Gamow-Teller 遷移で到達できるのは,中間状態の中も最も下の配位だけ

- 終状態から中間状態の中の最も下の配位への Gamow-Teller 遷移振幅(赤い矢印)は負の干渉

- 48Ca **→** 48Ti

- Gamow-Teller 巨大共鳴の主成分

- 48Ti → 48Sc の Gamow-Teller 遷移には巨大共鳴はない

**Courtesy of K. Muto **

## B(GT‐) と B(GT+) の負の相関

*B*(GT**‐**) と *B*(GT+) の負の相関

**巨大共鳴**

**Courtesy of K. Muto **

## Some concern by Amos, Faessler and Rodin

**Proportionality**

**Exercised by using:**
**76****Ge--****76****Se system**
**QRPA calculation**
**DWA**

**questioned.**

**Notes:**
1‘00
Let me summarize my talk. 
We measured the (p,n) and (n,p) reactions at 300 MeV to study the B(GT) distributions in 116In.

Multipole decomposition analysis has been carried out to identify the GT strengths in the continuum.

We identified the g.s. peak as 1+ state and the B(GT-) is obtained to be 0.26.

The partial matrix element through g.s. of 116In is 0.07, and this accounts for the half-life of 116Cd.

The B(GT+) distribution in the continuum is obtained for the first time.
Although there is a large uncertainty in subtraction of IVSM contribution, the present analysis gives an excellent agreement with a QRPA calculation.

That’s all. Thank you.

## Proportionality test by QRPA

- Amos, Faesler & Rodin, PRC76(2007)014614

- Transition density:  QRPA

- Reaction code:

- DW81

- The proportionality in the (n,p) channel looks worse.

- ... Sasano’s calc.

- Confirmed:

- (p,n)

- (n,p)

- ... but not so serious !

**Notes:**
This situation is similar to what was pointed out by Amos et al. for 76Ge

Dr. Sasano performed the calculation by using QRPA transition density of Feasler and Rodin, and obtained the same tendency 

## Proportionality test by Shell model 

**Exercise by using:**
**  ****48****Ca--****48****Ti system**
**  ****Shell model calculations**
**  ****Standard DWIA calc. **

**Deviations are large for small B(GT) for both sides.**

**Average (        ) works very well!**

- Sasano

- 48Ca(p,n)48Sc

- 48Ti(n,p)48Sc

- unit cross section (A.U.)

- B(GT-)

- B(GT+)

- 1

- 0.01

**Notes:**
1‘00
Let me summarize my talk. 
We measured the (p,n) and (n,p) reactions at 300 MeV to study the B(GT) distributions in 116In.

Multipole decomposition analysis has been carried out to identify the GT strengths in the continuum.

We identified the g.s. peak as 1+ state and the B(GT-) is obtained to be 0.26.

The partial matrix element through g.s. of 116In is 0.07, and this accounts for the half-life of 116Cd.

The B(GT+) distribution in the continuum is obtained for the first time.
Although there is a large uncertainty in subtraction of IVSM contribution, the present analysis gives an excellent agreement with a QRPA calculation.

That’s all. Thank you.

## Proportionality test-2 by Sasano 

**What is the reason of spread?**

**Exercise by using:**
**58****Ni system**
**Shell model calculations**
**Standard DWIA calc. **
**     ****with/without tensor interactions**

**Deviations are mainly due to the tensor interactions.**

- full int.

- wo tensor int.

**Notes:**
1‘00
Let me summarize my talk. 
We measured the (p,n) and (n,p) reactions at 300 MeV to study the B(GT) distributions in 116In.

Multipole decomposition analysis has been carried out to identify the GT strengths in the continuum.

We identified the g.s. peak as 1+ state and the B(GT-) is obtained to be 0.26.

The partial matrix element through g.s. of 116In is 0.07, and this accounts for the half-life of 116Cd.

The B(GT+) distribution in the continuum is obtained for the first time.
Although there is a large uncertainty in subtraction of IVSM contribution, the present analysis gives an excellent agreement with a QRPA calculation.

That’s all. Thank you.

## Results on

**Results on**
**116****Cd(p,n)****116****In,  ****116****Sn(n,p)****116****In  reactions**

## 116Cd(p,n) & 116Sn(n,p) results

|  | Present |  |  |
| --- | --- | --- | --- |
|  | 33±4 |  |  |
|  | 7±1 |  |  |
| IVSM subtracted | 4±1±.. |  |  |

- BB

- 116Cd(p,n) & 116Sn(n,p) results

**GT****-**

**GT****+**

- Sasano

- B(GT) distributions

- IVSM?

- dB(GT)/dEx (MeV-1)

**Notes:**
1’30-
Let me show you the result of 116Cd, only briefly. 
By the MD analysis, we obtained the B(GT) distribution for the (p,n) side and the (n,p) side.
Again the vertical scale is ten times different. 
Please note that the B(GT+) side shown here contains 2hw component called isovector spin monopole excitation, which is inseparable by the MD analysis.
The peak position of this spin monopole is predicted to be 18 MeV by Hamamoto and Sagawa. 

The integrated strengths are 33 and 7 up to 20 MeV excitation, and it becomes 4 when the IVSM contribution is estimated and subtracted.
A QRPA calculation by Alvarez-Rodriguez by deformed basis looks like this. 
The calculation gives a good prediction in the B(GT-) side, but it seems to underestimate the B(GT+) side.