Ab initio study of the photoabsorption of ${}^4$He

There are some discrepancies in the low-energy data on the photoabsorption cross section of ${}^4$He. We calculate the cross section with realistic nuclear forces and explicitly correlated Gaussian functions. Final-state interactions and two- and three-body decay channels are taken into account. The cross section is evaluated using two methods: With the complex scaling method the total absorption cross section is obtained up to the rest energy of a pion, and with the microscopic $R$-matrix method cross sections for both ${}^4$He($\gamma ,p$)${}^3$H and ${}^4$He($\gamma ,n$)${}^3$He are calculated below 40 MeV. Both methods give virtually the same result. The cross section rises sharply from the ${}^3\text{H}+p$ threshold, reaching a giant resonance peak at 26–27 MeV. Our calculation reproduces almost all the data above 30 MeV. We stress the importance of ${}^3\mathrm{H}+p$ and ${}^3\mathrm{He}+n$ cluster configurations on the cross section as well as the effect of the one-pion exchange potential on the photonuclear sum rule.

Figure 1

Three patterns for the dipole excitations for ${}^4$He. Thick solid lines denote the coordinates on which the spatial part of the $E1$ operator acts.

Figure 2

Discretized strength of the $E1$ transitions in ${}^4$He. See the text for the calculations classified by sp, $3N+N$, $d+p+n$, and Full.

Figure 3

Transition densities for the three discretized states listed in Table that have strong $E1$ strength.

Figure 4

Electric dipole strength functions obtained by using the CSM with different rotational angles $\theta$.

Figure 5

Comparison of the photoabsorption cross sections calculated with the CSM and the MRM.

Figure 6

Moments of the photoabsorption cross section as a function of the upper limit of the integration. The moments with the discretized states ($\theta =0^{\circ }$) are also plotted. The AV8${}^{\prime }$ $+$ 3NF potential is used. The units of $m_{\kappa }$ are mb MeV${}^{\kappa +1}$.

Figure 7

Photoabsorption cross sections of ${}^4$He$(\gamma ,p)$ ${}^3$H and ${}^4$He$(\gamma ,n)$ ${}^3$He reactions compared between the MRM calculation and experiment. Solid curve: AV8${}^{\prime }$ $+$ 3NF; dashed curve: G3RS $+$ 3NF. The thin dotted curve is the LIT calculation with the Malfliet-Tjon potential taken from Ref. [3]. The data are taken as follows: open circles [1], squares [5], closed circles [45], and triangles [2].

Figure 8

Ratio of the photoabsorption cross sections of ${}^4$He$(\gamma ,p)$${}^3$H and ${}^4$He$(\gamma ,n)$${}^3$He. The data are taken as follows: open circles [1], closed circles [45], and triangles [46].

Figure 9

Comparison of the photoabsorption cross section between the CSM calculation with $\theta ={17}^{\circ }$ and experiment. The data are taken as follows: closed triangles [43], squares [48], open circles [1], closed circles [45], and open triangles [4].

Figure 10

The photoabsorption cross section weighted by the intensity distributions of photons as used in the experiment [1, 45]. Solid and dotted curves are the original theoretical cross sections. Open and closed triangles are the weighted cross sections with AV8${}^{\prime }$ $+$ 3NF, while open and closed squares are the results with G3RS $+$ 3NF. Open and closed circles are the data taken from Refs. [1, 45].

Figure 11

Decomposition of the photoabsorption cross section into the $3N+N$ and other contributions. See the text for how the decomposition is made. The data are taken from Ref. [43].

Figure 12

Decomposition of the photoabsorption cross section into contributions specified by the total spin $S$. See the text for details.