# Low-lying Proton Intruder State in 13B

S. Ota  S. Shimoura  H. Iwasaki  M. Kurokawa  S. Michimasa  N. Aoi  H. Baba
K. Demichi  Z. Elekes  T. Fukuchi  T. Gomi  S. Kanno  S. Kubono  K. Kurita  H.
Hasegawa  E. Ideguchi  N. Iwasa  Y.U. Matsuyama  K.L. Yurkewicz  T. Minemura
T. Motobayashi  T. Murakami  M. Notani  A. Odahara  A. Saito  H. Sakurai  E.
Takeshita  S. Takeuchi  M. Tamaki  T. Teranishi  Y. Yanagisawa  K. Yamada  M.
Ishihara  Center for Nuclear Study, University of Tokyo, Saitama 351-0198,
Japan  Department of Physics, University of Tokyo, Tokyo 113-0033, Japan
RIKEN Nishina Center for Accelerator-Based Science, Saitama 351-0198, Japan
Department of Physics, Rikkyo University, Tokyo 171-8501, Japan  Hungarian
Acad. Sci., Inst. Nucl. Res., H-4001 Debrecen, Hungary  Department of Physics,
Tohoku University, Miyagi 980-8578, Japan  NSCL, Michigan State University,
East Lansing, MI 48824, USA  Department of Physics, Kyoto University, Kyoto
606-8502, Japan  Argonne National Laboratory, Argonne, IL 60439, USA
Department of Physics, Osaka University 560-0043, Japan  Department of
Physics, Kyushu University, 812-8581

###### Abstract

The neturon rich nucleus 13B was studied via the proton transfer reaction
4He(12Be,13B$\gamma$) at 50$A$ MeV. The known 4.83-MeV excited state was
strongly populated and its spin and parity were assigned to 1/2+ by comparing
the angular differential cross section data with DWBA calculations. This low-
lying 1/2+ state is interpreted as a proton intruder state and indicates a
deformation of the nucleus.

###### keywords:

Intruder state , Proton single particle state , Proton transfer reaction ,
4He(12Be,13B$\gamma$) ,

###### PACS:

21.10.Pc , 25.55.Hp , 27.20.+n , 29.30.Kv

††journal: Physics Letters B

The existence of intruder states in light neutron-rich unstable nuclei is
often considered to be evidence for one or more $\hbar\omega$ configurations
in the low-lying states around the $psd$ shell. The ground state of 11Be is
$1/2^{+}$ which is lower in energy by 0.3 MeV than the $1/2^{-}$ state [1]. In
12Be, there is a $1^{-}$ intruder state at 2.7-MeV excitation energy [2]. The
energies of these low-lying, non-normal parity states indicate $1\hbar\omega$
configurations. Furthermore, the presence of low-lying 2${}_{1}^{+}$ [3] and
0${}_{2}^{+}$ [4, 5] states in 12Be suggests a $2\hbar\omega$ configuration.

Three theoretical interpretations have been proposed for these one or more
$\hbar\omega$ configurations in the low-lying states of neutron-rich unstable
nuclei: (1) the monopole interaction of the tensor force [6], (2) the loosely
bound nature of some orbitals [7], and (3) nuclear deformation [5, 8, 9]. In
Ref. [6],the effective interaction was determined so that the model reproduces
the energy levels in light, neutron-rich nuclei including intruder states, and
the importance of monopole interaction due to the tensor force was pointed
out. Reference [7] discusses the fact that in the $psd$ shell, the $2s_{1/2}$
orbital gains its energy relative to the other orbitals due to its loosely
bound nature. The non-zero $\hbar\omega$ configurations can also be
intuitively explained by the deformed mean field picture. As seen in the
Nilsson diagram, the gap becomes smaller with increasing deformation [5, 8,
9]. Since the combination of these effects, which are provided by their
corresponding theoretical models, changes the neutron shell structure in
neutron-rich nuclei, such as 11,12Be, the relative importance of the three
theoretical approaches has not been clarified.

For the proton shell in light neutron-rich nuclei, the effects due to the
tensor force and the loosely bound nature of the orbitals are expected to be
small since the $\nu p_{1/2,3/2}$ orbitals are fully filled and the proton(s)
are deeply bound. However, deformation is still presumed to affect the proton
shell structure. Proton intruder states are, therefore, signatures for the
importance of deformation. In the present study, we focus on the proton shell
structure in the $N=8$ nucleus 13B by investigating the proton single-particle
states.

In order to investigate the proton single-particle states in 13B, we used the
$(\alpha,t)$ reaction on 12Be in inverse kinematics. This process at an
intermediate energy has a relatively large cross section since the proton to
be transferred is deeply bound in the $\alpha$ particle and, thus, has high-
momentum components, which reduce the effect of the momentum mismatch of the
($\alpha$,$t$) reaction [10].

The experiment was performed at the RIKEN Accelerator Research Facility. A
12Be beam was produced by the fragmentation reaction of a 100$A$ MeV 18O beam
on a 9Be target with a thickness of 1.85-g/cm2. The 12Be beam was separated by
the RIKEN Projectile-fragment Separator (RIPS) [12]. The incident particles
were identified on an event-by-event basis using the measured time-of-flight
and the energy deposited. The time-of-flight, over a path length of 5.4 m, and
the energy deposited were measured using two plastic scintillators located at
the last two foci of the RIPS. The intensity and the purity of the 12Be beam
respectively were typically 2 $\times$ 105 counts per second and 90%.

The 50$A$ MeV 12Be beam bombarded a secondary target of liquid helium[11]
located at the final focus of the RIPS. A liquid helium target was chosen
because of its statistical advantage in terms of the experimental yields. The
helium was condensed by a cryogenic refrigerator and kept below 4 K during the
experiment. A target thickness of 143$\pm$5 mg/cm2 was estimated from the
velocity difference between outgoing particles measured with and without the
liquid helium. The positions and directions of the incident particles on the
secondary target were deduced from the position information of two parallel
plate avalanche counters [13] located 30-cm apart from each other around the
final focus. The outgoing particles were detected by a plastic scintillator
hodoscope 3.5-m downstream from the secondary target with a 1 $\times$ 1 m2
active area and an angular acceptance of up to 8 degrees in the laboratory
frame. The plastic scintillator hodoscope consisted of 5-mm thick $\Delta E$
and 60-mm thick $E$ layers. The $\Delta E$ layer was divided into 13 plastic
scintillator bars vertically and the $E$ layer into 16 plastic scintillator
bars horizontally. The outgoing particles were identified on an event-by-event
basis using the measured time-of-flight and the energy deposited in the
$\Delta E$ and $E$ layers. The mass distribution for the $Z=5$ particles is
shown in Fig. 1; the mass resolution $(\delta A)$ was determined to be
$\sim$0.25. The time-of-flight between the secondary target and the hodoscope
was deduced from the time information of the plastic scintillators located
upstream from the secondary target and the plastic scintillator hodoscope.
Position information for the outgoing particles was deduced from the time
difference between the output signals from the two photomultiplier tubes
attached to both ends of each scintillator bar, and was used to determine the
scattering angle. The angular resolution of the scattering angle in the
laboratory frame was 0.5 degrees in one standard deviation.

The de-excitation $\gamma$ rays were detected by an array of germanium
detectors: Gamma-Ray detector Array with Position and Energy sensitivities
(GRAPE)[14]. This consisted of 6 germanium detectors located at 140∘ with
respect to the beam axis. Each detector contains two cylindrical crystals 6 cm
in diameter and 2 cm thick, with a common anode between them. The each cathode
attached to each crystal is segmented into a $3\times 3$ matrix. The GRAPE
provides position information of the $\gamma$-ray interaction point, which is
extracted from a pulse shape analysis of the signal from the cathode [14, 15].
The intrinsic energy resolution and the full energy peak efficiency were
typically 2.7 keV (FWHM) and 0.4%, respectively, for 1332-keV $\gamma$ rays
from a 60Co standard source. The energy resolution after correcting for the
Doppler shift was deduced to be 1.3% (FWHM) for 2.1-MeV $\gamma$ rays,
corresponding to the decay of the first 2+ state of 12Be moving with 30% the
light velocity. The excited states of 13B populated in the reaction were
identified by measuring the energy of the de-excitation $\gamma$ rays.

Figure 2 shows the energy spectrum of $\gamma$ rays measured in coincidence
with 13B after correcting for the Doppler shift. There are three peaks
corresponding to the transitions from (3.68-, 3.73-), 4.13- and 4.83-MeV
excited states to the ground state. The peaks seen in the low energy region is
considered to originate from the reaction of the beam and the window of the
target cell. Other significant transitions including those between the excited
states were not observed in the present measurement. In the figure, hatched
areas show the response functions of the GRAPE for the de-excitation $\gamma$
rays obtained by means of a Monte Carlo simulation using the GEANT4 code [16,
17] and for the background $\gamma$ rays. The background was assumed to
consist of two components, the natural background $\gamma$ rays, estimated by
putting the gate in the non-prompt region of the time spectrum of the GRAPE,
and the $\gamma$ rays from the isomer state of 12Be, which were simulated by
assuming a life time of 331 ns [5]. The ratio of the isomer state to the
ground state in the secondary beam was less than 2 percent at the secondary
target. In the simulations, all the resolutions of the detectors associated
with the correction for the Doppler shift were taken into account. The
intensity of each decay to the ground state was deduced by fitting the
experimental spectrum with the sum of the response functions and the
background. Assuming no cascade decay, the derived relative intensities of the
observed $\gamma$ rays from the known excited states are shown in Table 1,
together with the previously reported data including two neutron transfer
[18], neutron knockout [19], $\beta$-decay followed by neutron decay [20], and
multi-nucleon transfer [21]. In the present reaction, the excited state at
4.83 MeV is strongly populated relative to the other excited states, while it
is less excited in the other reactions except for the multi-nucleon transfer
reaction which is expected to populate proton excited states. Considering the
selectivity of the proton transfer reaction, it is conceivable that the
4.83-MeV excited state is of proton single-particle nature.

In order to determine the angular differential cross section of the
4He(12Be,13B∗) reaction, individual $\gamma$-ray spectra with 0.5-degree-
scattering-angle cuts were fitted with the same response functions and
background described above, and they were analyzed to deduce the populations.
Figure 3 shows the experimental angular distribution for the 4.83-MeV
excitation with filled circles. The transferred angular momentum ($\Delta L$)
in the reaction is determined by comparing the obtained angular distributions
with predictions of the distorted-wave Born approximations (DWBA), calculated
with the DWUCK5 code [22]. The optical potentials for the entrance and exit
channels were obtained by adopting a single folding model used in Ref. [23].
The density distribution of 12Be for the folding is calculated by using the
mean field calculation code, TIMORA[24, 25]. The density distribution of 13B
is assumed to be the same as that of 12Be with $R(^{13}{\rm B})/R(^{12}{\rm
Be})=(13/12)^{1/3}$. For the entrance channel, the depth of the imaginary
potential is adjusted so as to represent the inelastic scattering data of
12Be, excited to the $2^{+}_{1}$ state. For the exit channel, the depths of
the real and imaginary potentials are varied in order to estimate the
statistical error for the spectroscopic factor. The DWBA predictions with
$\Delta L=0,1,2$ are shown as curves in Fig. 3. The absolute magnitudes of the
predictions are normalized so as to minimize the $\chi^{2}$ values. The
reduced $\chi^{2}$ value is 0.74 for the $L=0$ calculation. The forward angle
peak in the experimental angular distribution is well described by the $\Delta
L$ = 0 DWBA calculation. Therefore, we assigned a spin and parity of 1/2+ to
the 4.83-MeV excited state. Its low energy indicates that it is a proton
intruder state from the $sd$ shell. The spectroscopic strength $C^{2}S$ was
deduced to be $0.20\pm 0.02$, where $S$ is a spectroscopic factor and $C^{2}$
is an isospin Clebsch-Gordan coefficient. The systematic errors of the
$C^{2}S$ due to the choice of the optical potentials in the DWBA calculation
and to the geometrical uncertainty of the GRAPE in the simulation were
evaluated to be 50% and 10%, respectively. The former one is obtained from the
difference between the folding model and a separate calculation using a global
optical potential for 12C in Ref. [26, 27]. In the absolute magnitude of the
differential cross section, there is no ambiguity originated from cascade
decays to or from the 4.83-MeV excited state. No excited state was found above
4.83 MeV up to the neutron threshold of 4.87 MeV in 13B, therefore, the
cascade decays to the 4.83-MeV excited state are unlikely to occur. On the
other hand, the cascade decay from the 4.83-MeV excited state is also small as
explained below. The excited state (1/2+) is expected to decay to the ground
state (3/2-) via an $E1$ transition, whose decay rate is proportional to the
cube of the transition energy, i.e., $E_{\gamma}^{3}$ [8]. The maximum
possible transition energy to a known excited state is 1.4 MeV corresponding
to the decay to the 3.48-MeV excited state. Even if the decay to this state is
by $E1$ transition, its decay rate is about 40 times smaller than to the
ground state. Decay rates other than $E1$ are also expected to be much
smaller. In fact, no cascade decay of the 4.83-MeV excited state was observed
in the present and the previous experiments.

There are few theoretical predictions for 13B. In Ref. [19], the result of a
shell model calculation for 13B has been shown, however, the calculation is
performed from the viewpoint of the neutron structure. Focusing on the proton
shell structure, we performed a shell model calculation for 13B(12Be) with the
calculation code, OXBASH [28], wherein the interaction including the effect of
the tensor force and reproducing intruder states in the neutron-rich nuclei
such as 11,12Be [6], is used. The model space consisting of the $psd$ shell
with maximum 3(2)$\hbar\omega$ excitation was considered for 13B(12Be). The
spectroscopic factor was calculated as the overlap between each excited state
of 13B and the ground state of 12Be. The shell model calculation predicts four
1/2+ states below 10 MeV excitation energy. Three lower states are predicted
at 3.7, 6.5 and 9.1 MeV with spectroscopic strengths of 0.01, 0.03 and 0.003,
respectively. These strengths are too small to explain the experimental
result. The fourth 1/2+ state with a spectroscopic strength of 0.30 is close
to the experimental spectroscopic strength; however its excitation energy is
9.5 MeV. These results of the shell model calculation may indicate that the
theoretical approach based on the effect of the tensor force does not explain
the experimental result, or the model space consisting of the $psd$ shell and
the excitation of 3$\hbar\omega$ are not large enough.

A simple expression for the observed $1/2^{+}$ state with proton single
particle nature is $(\pi sd)^{1}\otimes^{12}$Be. Concerning the possible large
deformation of 12Be, we examine the qualitative consequence of a deformed
core. The $1/2^{+}$ state arises with a configuration of
$(\pi[220\frac{1}{2}])^{1}$ to the 12Be(g.s.) core. As seen in the Nilsson
diagram, at large deformation, the $\pi[220\frac{1}{2}]$ orbital gains energy.
The energy gain of the total system compared to the spherical $s_{1/2}$ is
estimated to be around 7 MeV from the diagram and the semi-empirical mass
formula with a deformation parameter of 0.5. The discrepancy between the shell
model prediction mentioned above and the present result for the $1/2^{+}$
state is thus ascribed to a core deformation effect. In the present reaction,
the observed $1/2^{+}$ state is considered to be populated by the transfer of
a proton to the $\pi[220\frac{1}{2}]$ orbital. Hence, the low excitation
energy of the 1/2+ state suggests a deformed mean field. Since the proton is
transfered to the $[220\frac{1}{2}]$ orbital by an $s$-wave ($\Delta L=0$),
the spectroscopic factor of the spherical $2s_{1/2}$ component in the
$[220\frac{1}{2}]$ orbital, e.g. $S=0.273$ at $\delta=0.4$ [8], may also
reproduce the experimental result.

Based on the discussion above, the $1/2^{+}$ intruder state at 4.83 MeV is a
signature of a deformed field and indicates the importance of a deformation in
this nuclei. On the other hand, the ground state of 13B is supposed to be
spherical with a normal $p$-shell configuration [29]. The excitation of only
one proton thus changes the structure of the nucleus.

Recently an AMD calculation related to the experimentally assigned 1/2+ state
of 13B was carried out by Kanada-En’yo et al [30]. The calculation predicts a
largely deformed 1/2${}_{1}^{+}$ state with proton $1\hbar\omega$ excitation
and neutron $2\hbar\omega$ excitation. In the excited state, the last proton
occupies a molecular $\sigma$ orbital which has a density distribution similar
to the $[220\frac{1}{2}]$ Nilsson orbital. The 1/2${}_{1}^{+}$ state predicted
by AMD may correspond to the experimental one although the calculated
excitation energy is 8 MeV.

In summary, we have studied the proton transfer reaction on 12Be in inverse
kinematics. A spin and parity of $1/2^{+}$ for the 4.83-MeV excited state in
13B were assigned for the first time. A spectroscopic strength of $0.20\pm
0.02$ was also obtained with 60% systematic error. This state is interpreted
to be a proton intruder state from the $sd$-shell because of its non-normal
parity and small excitation energy. The nuclear deformation provides a simple
mechanism for the existence of such a low-lying proton intruder state. The
present study shows the importance of deformation for proton shell structure
in neutron-rich nuclei and the change of the proton shell structure deu to the
excitation of one proton.

We would like to thank the RIKEN Ring Cyclotron staff members for their
operation during the experiment. The present work was partially supported by
the Grant-in-Aid for Scientific Research (No.15204018) by the Ministry of
Education, Culture, Sports, Science and Technology, of Japan.

## References

  * [1] D. Wilkinson, et al., Phys. Rev. 113 (1959) 563.
  * [2] H. Iwasaki, et al., Phys. Lett. B 491 (2000) 8.
  * [3] H. Iwasaki, et al., Phys. Lett. B 481 (2000) 7.
  * [4] S. Shimoura, et al., Phys. Lett. B 560 (2003) 31.
  * [5] S. Shimoura, et al., Phys. Lett. B 654 (2007) 87.
  * [6] T. Suzuki, et al., Phys. Rev. C 67 (2003) 044302.
  * [7] I. Hamamoto, Nucl. Phys. A 731 (2004) 211.
  * [8] A. Bohr, B. R. Mottelson, Nuclear Structure, Vol. II, World Scientific (1998).
  * [9] I. Hamamoto, S. Shimoura J. Phys. G 34 (2007) 2715
  * [10] S. Michimasa, et al., Phys. Lett. B 638 (2006) 146.
  * [11] H. Ryuto, et al., Nucl. Instr. and Meth. A 555 (2005) 1.
  * [12] T. Kubo, et al., Nucl. Instr. and Meth. B 70 (1992) 309.
  * [13] H. Kumagai, et al., Nucl. Instr. and Meth. A 470 (2001) 562.
  * [14] S. Shimoura, Nucl. Instr. and Meth. A 525 (2004) 188.
  * [15] M. Kurokawa, et al., IEEE TRANSACTIONS ON NUCLEAR SCIENCE 50 (2003) 1309.
  * [16] S. Agostinelli, et al., Nucl. Instr. and Meth. A 506 (2003) 250.
  * [17] Geant4 a toolkit for the simulation of the passage of particles through matter, http://geant4.web.cern.ch/geant4/index.shtml.
  * [18] F. Ajzenberg-Selove, et al., Phys. Rev. C 17 (1978) 1283.
  * [19] V. Guimarães, et al., Phys. Rev. C 61 (2000) 064609.
  * [20] N. Aoi, et al., Phys. Rev. C 66 (2002) 014301.
  * [21] R. Kalpakchieva, et al., Eur. Phys. J. A 7 (2000) 451.
  * [22] P. D. Kunz, computer code DWUCK5, unpublished.
  * [23] G. R. Satchler, Phys. Rev. C 55 (1997) 285.
  * [24] C. J. Horowitz, Computational Nuclear Physics, Vol. I, Springer-Verlag (1991).
  * [25] C. J. Horowitz, Nucl. Phys. A 368 (1981) 503.
  * [26] A. Ingemarsson, et al., Nucl. Phys. A 676 (2000) 3.
  * [27] A. Ingemarsson, et al., Nucl. Phys. A 696 (2001) 3.
  * [28] B. A. Brown, A. Etchegoyen, W. D. M. Rae, The computer code OXBASH, MSU-NSCL report number 524 (1986).
  * [29] T. Nagatomo, et al., Nucl. Phys. A 746 (2004) 509c
  * [30] Y. Kanada-En’yo, et al., submitted to Phys. Rev C (arXiv:0706.3503v1 [nucl–th]).

Figure 1: Mass distribution of the outgoing particles for $Z=5$ extracted from the correlation between TOF and $\Delta E$ measured with the plastic scintillator hodoscope.  Figure 2:  Doppler corrected $\gamma$-ray spectrum in coincidence with 13B particles. The spectrum is decomposed with the sum of response functions of the GRAPE for the de-excitation and background $\gamma$ rays. The resulting responce functions are shown with hatched areas. The response functions for two doublets around 3.5 and 3.7 MeV are summed. The response function for the background includes the natrural background and the decay of the 12Be isomer (see the text).  Figure 3: Angular distribution of the 4.83-MeV excited 13B. Experimental data is shown by the filled circles with statistical errors. The solid, dotted and dashed curves show the DWBA predictions with assumptions of $\Delta L$ = 0, 1, and 2, respectively. See the text for more detail including the optical potentials.  Table 1: List of the relative populations of the excited states. The intensities are normalized by the most intense population. The errors are statistical only. In the last column, the spins and parities which have been assigned in the previous and present studies are listed. a:Present reaction of 4He(12Be,13B$\gamma$). b:11B (t,p)13B. c:9Be (14B,13B)X. d:14Be $\beta$ delayed n. e:16O(14C,17F)13B. For the reaction b the relative intensity is at $\theta_{\rm lab}=10^{\circ}$ and for the reaction e at $\theta_{\rm c.m.}=5.4^{\circ}$.  | Relative intensities |
---|---|---
Ex (MeV) | a | b | c | d | e | $J^{\pi}$
3.48 | 0.19 $\pm$ 0.05 | 0.06 | 0.60 $\pm$ 0.14 |  |  |
3.53 | 0.20 $\pm$ 0.05 | 0.19 |  | 1 |  |
3.68 | 0.74 $\pm$ 0.07 | 0.38 | 1 |  |  |
3.71 | 0.68 $\pm$ 0.07 | 0.25 |  |  |  |
4.13 | 0.49 $\pm$ 0.04 | 1 | 0.04 $\pm$ 0.04 |  |  |
4.83 | 1 | 0.03 |  |  | 1 | 1/2+