Ab initio study of the $J^{\pi }=0^{\pm }$ continuum structures in ${}^4\mathrm{He}$

The $J^{\pi }=0^{\pm }$ continuum structures in ${}^4\mathrm{He}$ are investigated by using an ab initio reaction theory with the microscopic $R$-matrix method. In the $E_x\ge \sim 20$ MeV excitation energy region of ${}^4\mathrm{He}$, the continuum states are mainly described by the $t+p$, $h+n$, and $d+d$ channels. The $J^{\pi }=0^{\pm }$ elastic phase shifts of the $t+p$ and $h+n$ channels show an apparently resonant behavior which might indicate the existence of excited $0_3^{+}$ and $0_2^{-}$ resonance states of ${}^4\mathrm{He}$ above the known $0_2^{+}$ and $0_1^{-}$ ones. However, the corresponding $0_3^{+}$ and $0_2^{-}$ resonances have not been observed yet, although an experimental candidate with a large decay width is reported for $0_2^{-}$. In this paper, by analyzing the $J^{\pi }=0^{\pm }S$ matrices, we discuss why the observation of these states is unlikely.

Figure 1

$0^{+}$ elastic phase shifts obtained with the $\mathrm{AV}{8}^{\prime }$+3NF interaction: $t+p$ (full line), $h+n$ (dashed line), and $d+d$ (dotted line) as a function of the $t+p$ center-of-mass energy.

Figure 2

Magnitudes ${\eta }_{\alpha }$ of the $S$ matrix of $0^{+}$ obtained with the $\mathrm{AV}{8}^{\prime }$+3NF interaction.

Figure 3

Argand plot of $S_{12}^{0+}$. The initial channel is $t+p$ and the final channel is $h+n$.

Figure 4

$0^{+}$ eigenphases. The elastic phase shifts in Fig. 1 are also plotted for comparison.

Figure 5

$0^{-}$ elastic phase shifts obtained with the AV8'+3NF interaction: $t+p$ (full line), $h+n$ (dashed line), and $d+d$ (dotted line).

Figure 6

Magnitudes ${\eta }_{\alpha }$ of the $S$ matrix for $0^{-}$ obtained with the AV8'+3NF interaction.

Figure 7

Argand plot of $S_{12}^{0-}$. The initial channel 1 is $t+p$ and the final channel 2 is $h+n$.

Figure 8

$0^{-}$ eigenphases. The elastic phase shifts in Fig. 5 are also plotted for comparison.