Session EL: Nuclear Structure IV

Excitations of $^4$He induced by electro-weak interactions

$^4$He is the lightest closed shell nucleus which has several excited states above the excitation energy of 20 MeV. We have recently reported that all the observed levels below 26 MeV are well reproduced in a full four-body calculation using realistic interactions (Phys. Rev. C {\bf 78}, 034305 (2008)). It is very interesting to extend this approach in order to study some excitations in $^4$He. In the energy region around 26 MeV, photoabsorption reaction occurs mainly through the electric dipole transition. The current experimental situation is controversial. Some experiments show different cross sections. Because there are only few theoretical studies on the dipole strength starting from a realistic interaction, further theoretical study may help clarify the situation. A study of neutrino-nucleus reaction is important to the scenario of a supernova explosion. In the final stage of a core collapse supernova, $^4$He is exposed to intense flux of neutrino. The $\nu$-$^4$He reaction is expected to play a significant role, and the reaction rate is proportional to the weak responses, for example, due to Gamow-Teller, spin-dipole, etc. operators. In this contribution, we will discuss electro-weak responses from the ground state of $^4$He to its continuum states by performing a full four-body calculation using realistic interactions. The photo-absorption and $\nu$-$^4$He reaction cross sections are discussed.   

Resonances of He isotopes using complex scaling method

We investigate the properties of resonances of He isotopes, in particular, $^6$He, $^7$He and $^8$He. We describe the He isotopes with the cluster model of $^4$He+$n$+$n$+$n$+$n$. The many-body resonances (for example, five-body resonances of $^8$He) and non-resonant states are described within the correct boundary condition using the complex scaling method. We discuss and predict the energy spectra and decay widths of resonances of He isotopes. We also investigate the characteristics of the structures of each resonances. such as the spectroscopic factors, configuration mixing. In $^7$He, we derive the spectroscopic factors of $^6$He+$n$ component of the obtained resonances, and also evaluate the corresponding strength functions of one-neutron removal reaction into $^6$He. It is found that the $^6$He(2$^+$) resonance gives the dominant contribution in the strength. Non-resonant contributions of $^5$He+$n$ and $^4$He+$n$+$n$ are very small.   

Structure of the neutron-rich isotope $^{13}$B with $N$~=~8 studied via lifetime measurements with low-energy fusion reactions

We report recent experimental studies on the structure of the neutron-rich isotope $^{13}$B with $N$~=~8 performed at the FN Tandem facility of the University of Cologne [1]. The lifetime measurements of the excited states in $^{13}$B were performed by the Doppler-shift attenuation method with the $^{7}$Li($^{7}$Li,$p$)$^{13}$B reaction at a beam energy of 5.4~MeV. To select the reaction channel unambiguously, and hence reduce the background considerably, the particle-$\gamma$ coincidence was employed. An anomalously long mean lifetime of 1.3(3)~ps was found for the excited state at 3.53~MeV in $^{13}$B. The hindered transition strengths between the ground and 3.53-MeV states clearly indicate significant intruder configurations for the excited state. The data are well explained by recent shell model calculations which suggest $J^{\pi}$~=~3/2$^{-}$ for the 3.53-MeV state with the dominant intruder ($\nu$2$p$2$h$) configuration, pointing to the fading effects of the $N$~=~8 shell closure. The occurrence of the intruder configurations in the $N$~=~8 isotones will be discussed. \\[0pt] [1]~H.~Iwasaki {\it et al.}, Phys. Rev. Lett. {\bf 102}, 202502 (2009).   

Proportionality between (t,3He) reaction differential cross sections and Gamow-Teller strengths.

The so-called unit cross section describing the proportionality between differential cross sections and Gamow-Teller transition strengths is studied for the case of the (t,$ ^{3}$He) charge-exchange reaction. Experimental data for H, and $ ^{12,13} $C targets taken at 115 AMeV are complimented by existing data for $ ^{2} $H, $ ^{6} $Li, and $ ^{26} $Mg. The (t,$ ^{3} $He) results are compared with results for the ($ ^{3} $He,t) reaction at 140 AMeV and for targets with 12 [Preview Abstract]

Recoil Distance Method Lifetime Measurement of the First 2$^{+}$ State in $^{18}$C

Electromagnetic transition rates can be directly obtained from lifetime measurements and shed light on the evolution of nuclear structure as one proceeds further from the the valley of stability. Recoil Distance Method lifetime measurements have been successfully carried out at NSCL through the coupling of the Segmented Germanium Array and the NSCL/K\"{o}ln plunger [1]. During a recent NSCL campaign, the collectivity and shape evolution of neutron-rich carbon isotopes were studied by lifetime measurements of the $2^{+}_{1}\rightarrow 0^{+}$ transition in $^{16,18,20}$C. Excited states in $^{18}$C were populated by a one-proton knockout at the target position of the S800 spectrograph. Particle-gated gamma-ray spectra were collected at five plunger target-degrader separation distances. The results of the lifetime measurement for $^{18}$C will be presented.\\[4pt] [1] K. Starosta {\it et al.}, Phys. Rev. Lett. {\bf 99}, 042503 (2007).   

Short-Range Correlations from $^{12}$C(e,e$^{\prime}$n)/$^2$H(e,e$^{\prime}$n)

The data analysis of the semi-inclusive channel of one of the kinematics of the Short-Range Correlations experiment E01-015 in Hall A at Jefferson Laboratory is in progress. The kinematics involved has a beam energy of 4.6 GeV, an energy transfer of 0.9 GeV, a $Q^2$ of 2 GeV$^2$/c$^2$, and a wide x$_b$ (Bjorken x) coverage around 1.2. In this analysis we are looking at backward going neutrons for each detected electron. The reactions being analyzed are $^{12}$C(e,e$^{\prime}$n) and $^2$H(e,e$^{\prime}$n) in order to calculate the cross-section ratio $^{12}$C(e,e$^{\prime}$n)/$^2$H(e,e$^{\prime}$n). We compare this ratio with the result of inclusive reaction's ratio $^{12}$C(e,e$^{\prime}$)/$^2$H(e,e$^{\prime}$). We see a clear dip at x$_b$ =1 and a flat region at x$_b>$1.4 for the inclusive data. Due to the scarcity of semi-inclusive data in the region of x$_b>$1.3, we cannot see the flat region, but the shape of available data in the two cases appear to be matching. The flat region is believed to be due to the two nucleon short-range correlations. The method of analysis and the recent results will be presented.   

Algebraic N-$\alpha$ model (applications for $^{12}$C)

Algebraic nuclear models have successively applied for various mass regions. Its semi-microscopic treatment has been applied for light nuclei like $^{12}$C where the Pauli principle between each cluster is completely taken into account. However, the method does not have been used directly for decay information. Therefore, we extend this algebraic method and investigate the structure of $^{12}$C. We use the model space expanded by Pauli allowed states (PAS) [H. Horiuchi, PTP58 204 (1977)] with orthogonality condition model (OCM). One advantage of this method is that we can generate infinite number of PAS by operating $Sp2R_z$ generators [K. Kato et al., PTP76 75 (1985)] from its band head state. Therefore, the group theoretical relation for each state becomes clear. We can see that the large electromagnetic transition strength appears in the same band states. This affects total expectation values, which we calculated by using truncated model space of SU3. In order to investigate their decay information, we use complex scaling method (CSM). Firstly, we check consistency of PAS method and CSM for alpha-alpha cluster system. As a next step, we combine this PAS method with CSM for $^{12}$C.   

Three $\alpha$ linear-chain structure in $^{13}$C

The realization of linear-chain configurations of $\alpha$ clusters has been a long-standing subject of nuclear structure study. Recently, the linear-chain structure has been discussed in $N>Z$ C isotopes, and candidates for that structure have been suggested in $^{13}$C based on the systematic search of multi-particle transfer reactions. In the past, the linear-chain structure was suggested for $0_2^+$ state of $^{12}$C, which is now recognized as an $\alpha$-condensed state. It is interesting to investigate how the additional one neutron change this structure and other cluster states in $^{12}$C, and whether the linear-chain structure is stabilized or not. We have investigated the structure of $^{13}$C focusing on the linear-chain structure of 3$\alpha$ cluster by using a microscopic 3$\alpha$+n model. We describe the 3$\alpha$ wave function by using the generator coordinate method (GCM), and the neutron wave function is optimized for each basis of GCM. In this talk, structures of several rotational bands obtained in this calculation are analyzed, and the realization of the linear-chain structure is discussed.   

$^{10}$Be+$\alpha$ correlation in $^{14}$C

We will report structure of excited states in $^{14}$C while paying attention to $^{10}$Be$+\alpha$ correlation. In the stable carbon nucleus, $^{12}$C, it is already known that various 3 $\alpha$ cluster structures appear in the excited states. It is natural to expect that rich phenomena may appear also in $^{14}$C which is an unstable neutron-rich nucleus. Many experiments indicate that there are various clustering structures in excited states of $^{14}$C. In these structures, a $^{10}$Be+$\alpha$ structure attracts much interest in association with a linear-chain structure of 3 $\alpha$ that has been studied for many years. For the systematic study of $^{14}$C, we adopted AMD(Antisymmetrized Molecular Dynamics) which has proved to be a powerful approach to describe various structures. The configurations were superposed in the GCM framework using ($\beta$, $\gamma$) as the generator coordinates. As the results, we obtained various states which have characteristic structures such as a triaxial structure, an equilateral-triangular structure and a linear-chain structure. We examined the possibility of the existence of $^{10}$Be+$\alpha$ correlation in these states. In linear-chain states, it was suggested that strong $^{10}$Be+$\alpha$ correlation exists, and this correlation plays an important role to stabilize the linear-chain structure.   

Lifetime measurements in $^{16}$C and $^{20}$C

The search for new phenomena and structure effects due to the influence of large isospin, weak nucleon binding, and coupling to the continuum is of great interest in nuclear structure physics. We present data from a direct lifetime measurement of the $2^+$ states in $^{16}$C and $^{20}$C, which have been cited as examples of ``neutron decoupling.'' The deduced B(E2:2$^+ \rightarrow 0^+$) values are compared to shell model calculations. Neutron-rich carbon nuclei are one of the few isotopes experimentally accessible up to the neutron drip-line and provide an opportunity to follow changes in structure from stability to the drip-line. The experiments were carried out at the NSCL using the recoil distance method. This work is a collaboration between LBNL, MSU/NSCL, and Cologne.   

Search for Alpha particle Condensation in $^{16}$O

Recently, Tohsaki \textit{et al} were proposed the $\alpha $ particles condensed state existed in the vicinity of the threshold energy that decay into 3- and 4-$\alpha $ particles in the $^{12}$C and $^{16}$O nuclei.The energy state of the 4-$\alpha $ particles condensation has not been specified yet in $^{16}$O though it is considered that the second 0$^{+}$ state (7.65MeV) in $^{12}$C is the 3-$\alpha $ particles condensed one theoretically. To verify the existence of the $\alpha $ condensation in $^{16}$O, we have performed the experiment on the $^{12}$C($^{16}$O,$^{16}$O*[X+$\alpha $]) $^{12}$C reaction. The probability of the 4-$\alpha $ particles condensed state of $^{16}$O decays to 3-$\alpha $ condensed one of $^{12}$C and an $\alpha $ particle is large.Therefore,we investigate the excited state in $^{16}$O by obtaining the branching ratio of each decay channel of $^{16}$O*$\to ^{12}$C (0$_{2}^{+})+\alpha $,$^{ 16}$O*$\to ^{12}$C (2$_{1}^{+})+\alpha $,$^{ 16}$O*$\to ^{12}$C (g.s) +$\alpha $.In this talk, We will report on result of the experiment and the MonteCalro simulation in $^{16}$O for excited state of 15.1MeV which was one of candidates for the 4-$\alpha $ condensation.