Emergence of nuclear clustering in electric-dipole excitations of ${}^6\mathrm{Li}$

Nuclear clustering plays an important role, especially in the dynamics of light nuclei. The importance of the emergence of the nuclear clustering was discussed in the recent measurement of the photoabsorption cross sections as it offered the possibility of the coexistence of various excitation modes which are closely related to the nuclear clustering. To understand the excitation mechanism, we study the electric-dipole ($E1$) responses of ${}^6\mathrm{Li}$ with a fully microscopic six-body calculation. The ground-state wave function is accurately described with a superposition of correlated Gaussian (CG) functions with the aid of the stochastic variational method. The final-state wave functions are also expressed by a number of the CG functions including important configurations to describe the six-body continuum states excited by the $E1$ field. We found that the out-of-phase transitions occur due to the oscillations of the valence nucleons against the ${}^4\mathrm{He}$ cluster at the low energies around 10 MeV indicating “soft” giant-dipole-resonance (GDR)-type excitations, which are very unique in the ${}^6\mathrm{Li}$ system but could be found in other nuclear systems. At the high energies beyond $\sim 30$ MeV typical GDR-type transitions occur. The ${}^3\mathrm{He}-{}^3\mathrm{H}$ clustering plays an important role to the GDR phenomena in the intermediate-energy regions around 20 MeV.

Figure 1

Point-matter densities of ${}^6\mathrm{Li}$ with different values of the $u$ parameter in the MN potential. The densities of $\alpha , h$, and $t$ with $u=0.93$ are also plotted for comparison.

Figure 2

Schematic figures of the basis functions for the final-state wave functions. Colored and uncolored small circles represent protons and neutrons, respectively. Thick lines indicate the coordinates excited by the $E1$ operator. See text for exact definitions.

Figure 3

Electric-dipole strengths of ${}^6\mathrm{Li}$ with the full model space with (a) $u=1.00$, (b) 0.93, and (c) 0.87. Arrows indicate the theoretical $\alpha +d, \alpha +p+n$, and $h+t$ thresholds from left to right, respectively.

Figure 4

Electric-dipole strengths of ${}^6\mathrm{Li}$ with the full model space with $u=0.93$ categorized by the amount of the spectroscopic factors into three: (a) $S_{\alpha pn}^2>0.80$, (b) $S_{ht}^2>0.5$, and (c) neither (a) nor (b). See text for details. Arrows indicate the theoretical $\alpha +d, \alpha +p+n$, and $h+t$ thresholds from left to right, respectively.

Figure 5

Transition densities of ${}^6\mathrm{Li}$ with the excitation energy of (a) 12.1, (b) 22.8, (c) 23.3, (d) 30.6, (e) 33.0, and (f) 34.6 MeV selected from Table 2. See text for details. Note that left panels plot the transition densities with the states having large $S_{\alpha pn}^2\approx 1$. Vertical thin lines indicate theoretical nuclear radii, $\sqrt{\frac{5}{3}}{r}_m$, with $r_m=1.41$ and 2.33 fm for ${}^4\mathrm{He}$ and ${}^6\mathrm{Li}$, respectively.

Figure 6

Comparison of the photoabsorption cross sections of ${}^6\mathrm{Li}$. Experimental ${}^6\mathrm{Li}(\gamma ,n)$ data are plotted as open rectangles [18], closed rectangles [43], open triangles [44], and inverted open triangles [45]. Since they are unavailable, most of error bars of the experimental data in Refs. [18, 45] are not plotted. Diamonds are the cross sections taken from Ref. [46], where the contributions of the $h+t$ and $p+d+t$ channels are analyzed and taken into account. Open circles denote the ${}^6\mathrm{Li}(\gamma ,n)+{}^6\mathrm{Li}(\gamma ,2n)+{}^6\mathrm{Li}(\gamma ,3n)$ data taken from Ref. [17].

Figure 7

Isoscalar dipole strengths of ${}^6\mathrm{Li}$ as a function of the excitation energy. Arrows indicate the theoretical $\alpha +d, \alpha +p+n$, and $h+t$ thresholds from left to right, respectively.

Figure 8

Electric-dipole strengths only with (a) $\alpha +p+n$ and (b) $h+t$ final-state configurations. Arrows indicate the theoretical $\alpha +d, \alpha +p+n$, and $h+t$ thresholds from left to right, respectively.

Figure 9

Transition densities to the states that give the prominent $E1$ strength only with the restricted model spaces: The $\alpha +p+n$ final-state configurations at (a) $E_x=14.5$, (c) 20.3, and (e) 31.7 MeV, and the $h+t$ final-state configurations at (b) $E_x=23.9$ and (d) 35.4 MeV. See the text for details. Vertical thin lines indicate theoretical nuclear radii, $\sqrt{\frac{5}{3}}{r}_m$, of ${}^4\mathrm{He}$ and ${}^6\mathrm{Li}$, respectively.

Figure 10

Cumulative sum of the $E1$ transition strengths of ${}^6\mathrm{Li}$ with the full model space, $\alpha +p+n$, and $(\alpha +p+n)+(h+t)$ configurations with $u=0.93$. The NEWSR value and the total sum of the $E1$ strengths only with the $\alpha +p+n$ configurations are plotted as thin dotted lines for comparison. See text for details. Arrows indicate the theoretical $\alpha +d, \alpha +p+n$, and $h+t$ thresholds from left to right, respectively.