I. HIGHLIGHTS OF THE YEARRIKEN Accel. Prog. Rep. 54 (2021)

RIKEN Accel. Prog. Rep. 54 (2021)

Probing alpha clusters in the low-density region of the nuclear surface†
J. Tanaka,∗1 Z. H. Yang,∗2 S. Typel,∗3,∗4 and T. Uesaka∗1 for the RCNP (p, pα) Collaboration

Alpha knockout reaction
protonGrand Raiden
Spectrometer
proton detection

neutron skin

Tin target
proton beam

0 1 2 3malpha particle
Large-AcceptanceSpectrometeralpha-particle detection

Fig. 1. Schematic illustration of the experimental setup.
†∗1∗2∗3∗4100060800
600

20 40

400002002080

1160Sn(p, pα)

112

Cd80

dσ/dMX (pb / MeV)

60
40200d010MX (MeV)

20200

116

80

Sn(p, pα)112Cd

60
40
20020040600

4000.50.4200experiment

0Theory
Thicker neutron skintheoryExperiment Less alpha clusters

58-30

d62-2066 -10 70

0 74 10 78
M (MeV)

20X
Neutron number

124

80Nα

120

116

20400

112

30

Sn(p, pα)120Cd

108

0.1

Sn(p, pα)

120

Cd

400
200

X0.6

800
600

0.40.20-20-10010MX (MeV)

20300.0112116120Mass number A1241) G. Gamow, Z. Phys. 51, 204 (1928).
2) S. Typel et al., Phys. Rev. C 81, 015803 (2010).
3) S. Typel, Phys. Rev. C 89, 064321 (2014).
4) M. Fujiwara et al., Nucl. Instrum. Methods Phys. Res.
A 422, 484 (1999).
5) J. Tanaka et al., Science 371, 260 (2021).

- S21 -400

00.00124

800

2000a0 scattered proton is analyzed
by0 the Grand Raiden
gal-20spectrometerat10an 20angleof40 45.3◦ .-30 A -20knocked-out-10010-30-20-10030
M (MeV)M (MeV)pha particle is analyzed by the LAS spectrometeratan angle of 60.0◦ .
The momenta of scattered protons and knockedout alpha particles were analyzed with the GrandRaiden spectrometer4) and a large acceptance spectrometer, respectively. The missing-mass spectra ofSn(p, pα)Cd reactions were constructed from these momenta, and strong transitions from the ground state of
Sn to the vicinity of the ground state of Cd were observed. Figure 2 shows (a) the missing-mass spectrumof 112 Sn(p, pα)108 Cd. The peak indicated by the arrow is the transition from the ground state of 112 Sn
to the vicinity of the ground state of 108 Cd. Figure 2(b) shows the isotope dependence of cross sections.5) The black filled circles indicate experimental
data, and the red open squares indicate theoretical predictions, where the theoretical alpha-cluster formation
probabilities were converted to the (p, pα) cross sections using nuclear reaction calculations based on thedistorted wave impulse approximation. A good agreement with the theoretical conjecture is observed.
The theoretical study further suggested not only thecontrol of the formation of alpha clusters by neutronskins, but also the suppression of neutron skins by theappearance of alpha clusters. The series of experimental studies of surface alpha clusters have the potential
to revise the parameters correlated with the neutronskin thickness in the nuclear equation of state in thefuture.
20040600

20References

Condensed from the article in Science 371, 260 (2021)
RIKEN Nishina Center
Research Center of Nuclear Physics, Osaka University
Technische Universität Darmstadt, Fachbereich Physik, Institut für Kernphysik
GSI Helmholtzzentrum für Schwerionenforschung GmbH0Sn(p, pα) CdFig. 2. (a) Missing-mass spectrum of60the0.3
reaction.
(b) Neutron-number
dependence of theSn(p, pα) Cd4040200(p, pα) reaction cross sections.
600
0.260

Cd200.00

400116400.05f

Sn(p, pα)

0.15

0.10

4000X

80

30

Counts / MeV-10

Counts / MeV

c-20

Excitation energy of 108Cd (MeV)Counts / MeV

dσ/dMX (pb / MeV)

-30

dσ/dMX (pb / MeV)

0800

12060-20040b

1000

Thinner neutron skinMore alpha clusters

80(b)

1200

040060201400 0.20

600-200ce1600

Counts per 1 MeV

1200Counts per 1 MeV

1600

dσ/dMX (pb / MeV)

Cd

13040

Counts per 1 MeVb108

Counts per 1 MeV

40

Sn(p, pα)1121081400
112Sn(p,pα)
CdSn(p, pα)108Cd

dσ/dMX (pb / MeV)

dσ/dMX (pb / MeV)

Cross section(pb/MeV)dσ/dMX (pb/ MeV)

60

112(a)σ (nb)
Cross section
(nb)

80

σ/Nα (nb)a80Counts / MeV

adσ/dMX (pb / MeV)

The formation of alpha clusters in the ground stateof heavy nuclei has been unclear for many years, boththeoretically and experimentally. Although the existence of preformed alpha particles in alpha-decay nuclei is an essential element in the theory of alpha decay,1) it was challenging to explain the appearance ofalpha clusters with the conventional mean-field models. In recent years, theoretical research based on thegeneralized density functional made progress and predicted that alpha clusters can exist in the low-density
region of the nuclear surface.2) It was shown that theformation amplitudes of alpha clusters on the nuclear
surface of tin isotopes decrease monotonically with increasing neutron excess, and the formation amplitudeof 124 Sn is approximately half that of 112 Sn.3) To directly prove the existence of alpha clusters in the surface of nuclei, the quasi-free alpha knockout reaction
is appropriate.
Our group performed an experiment at the ResearchCenter for Nuclear Physics of Osaka University. A proton beam at 392 MeV generated at the cyclotron facility bombarded stable tin targets (112 Sn, 116 Sn, 120 Sn,124Sn) with an intensity of 100 nA. To achieve the highprecision measurement of knocked-out alpha particles,
we used double-arm spectrometers. The experimental setup is shown in Fig. 1. A proton beam impinges
on a tin target (red arrow from the left). Following aA
Sn(p, pα)A−4 Cd reaction (emphasized in the inset),