Harmonic-oscillator excitations of precise few-body wave functions

A method for calculating the occupation probability of the number of harmonic-oscillator (HO) quanta is developed for a precise few-body wave function obtained in a correlated Gaussian basis. The probability distributions of two- to four-nucleon wave functions obtained by using different nucleon-nucleon ($NN$) interactions are analyzed to gain insight into the characteristic behavior of the various interactions. Tensor correlations as well as short-range correlations play a crucial role in enhancing the probability of high HO excitations. For the excited states of ${}^4\mathrm{He}$, the interaction dependence is much less because high HO quanta are mainly responsible for describing the relative-motion function between the $3N+N$ (${}^3\mathrm{H}+p$ and ${}^3\mathrm{He}+n$) clusters.

Figure 1

$\hslash \omega$ dependence of the occupation probability of the lowest HO quantum in the ground state of ${}^4\mathrm{He}$. The arrow indicates the $\hslash \omega$ value that is employed to calculate $P_Q$ values of ${}^4\mathrm{He}$. See text for detail.

Figure 2

Occupation probability distributions of the total HO quanta for the ground state of ${}^4\mathrm{He}$ calculated with different potential models. $P_0$ is not shown in the figure but given in Table 1. $P_Q$ values are connected by dotted lines to guide the eye.

Figure 3

Angular-momentum decomposition of the occupation probability of the total HO quanta for the ground state of ${}^4\mathrm{He}$. $P_0^L$ values are 79.1%, 0%, 0% for $L=0,1,2$, respectively. The $\mathrm{AV}{8}^{\prime }+3\mathrm{NF}$ potential is used.

Figure 4

$\hslash \omega$ dependence of the occupation probability of the total HO quanta with $Q>0$ for the ground state of ${}^4\mathrm{He}$. The $\mathrm{AV}{8}^{\prime }+3\mathrm{NF}$ potential is used.

Figure 5

Occupation probability distributions of the total HO quanta for the first-excited state of ${}^4\mathrm{He}$.

Figure 6

$\hslash \omega$ dependence of the occupation probability of the total HO quanta for the first-excited state of ${}^4\mathrm{He}$. The $\mathrm{AV}{8}^{\prime }+3\mathrm{NF}$ potential is used.

Figure 7

Occupation probability distributions of the HO quanta for the excited states of ${}^4\mathrm{He}$. The $\mathrm{AV}{8}^{\prime }+3\mathrm{NF}$ potential is used.