Investigation of the ${}^9\mathrm{B}$ nucleus and its cluster-nucleon correlations

In order to study the correlations between clusters and nucleons in light nuclei, we formulate a new superposed Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function which describes both spatially large spreading and cluster-correlated dynamics of valence nucleons. Using this new THSR wave function, the binding energy of ${}^9\mathrm{B}$ is significantly improved in comparison with our previous studies. We calculate the excited states of ${}^9\mathrm{B}$ and obtain an energy spectrum of ${}^9\mathrm{B}$ which is consistent with the experimental results. This includes the prediction of the first $1/2^{+}$ excited state of ${}^9\mathrm{B}$ which is not yet fixed experimentally. We study the proton dynamics in ${}^9\mathrm{B}$ and find that the cluster-proton correlation plays an essential role for the proton dynamics in the ground state of ${}^9\mathrm{B}$. Furthermore, we discuss the density distribution of the valence proton with special attention to its tail structure. Finally, the resonance nature of excited states of ${}^9\mathrm{B}$ is illustrated comparing root-mean-square radii between the ground and excited states.

Figure 1

Theoretical and experimental results of the energy spectrum of ${}^9\mathrm{B}$. The thresholds are set at the origin of the vertical axis.

Figure 2

Energy curve of the ground state of ${}^9\mathrm{B}$ with respect to the ratio $d/c$, while other parameters are fixed to be the same as the optimized superposed THSR wave function.

Figure 3

Density distributions of the valence proton of ${}^9\mathrm{B}$ in the $y=0$ cross section obtained with different THSR wave functions. The left figure corresponds to traditional THSR wave function. The right one corresponds to the new THSR wave function. The unit of the density is ${\mathrm{fm}}^{-3}$.

Figure 4

Density distributions of the valence proton obtained with different terms in the new superposed THSR wave function. The left corresponds to the cluster-correlated term ${\mathrm{\Phi }}_1$. The right corresponds to the large spreading configuration ${\mathrm{\Phi }}_0$. Parameter $\beta \mathrm{s}$ are selected as the optimized values of the new superposed THSR wave function. The unit of the density is ${\mathrm{fm}}^{-3}$.

Figure 5

The angular-averaged density distributions of the valence proton. The dashed (blue) line is obtained with the traditional THSR wave function while the full (red) line is obtained with the new THSR wave function.

Figure 6

The excitation energy of the $1/2^{+}$ state in ${}^9\mathrm{B}$ with increasing sample size (${10}^6$) in our Monte Carlo calculation. The dotted line denotes the experimental prediction in Ref. [26].

Figure 7

The excited energy of the $1/2^{+}$ state of ${}^9\mathrm{B}$ with our new superposed THSR wave function (line) compared with various experimental results (dots). The experimental results are from MCB 1954 [33], Saji 1960 [34], ST 1962 [35], SBM 1967 [36], KB 1967 [37], ACF 1988 [38], SFA 2011 [39], TKG 2004 [26].

Figure 8

Theoretical and experimental energy spectra of ${}^9\mathrm{B}$. The states with higher energy, which are found in experiment, are not considered in our calculation because of the limitation of computation power.