Systematic analysis of breakup reactions with $t$ and ${}^3\mathrm{He}$ projectiles

Background: Systematic measurement of $t$ and ${}^3\mathrm{He}$ knockout processes is planned. The weakly-bound nature of these nuclei may affect the interpretation of forthcoming knockout reaction data.

Purpose: We aim at clarifying breakup properties of $t$ and ${}^3\mathrm{He}$ by investigating their elastic and breakup cross sections.

Methods: We employ the four-body continuum-discretized coupled-channels method with the eikonal approximation to describe the reactions with $t$ and ${}^3\mathrm{He}$ projectiles.

Results: The breakup cross section of $t$ is found to be almost the same as that of ${}^3\mathrm{He}$ and is about one-third of that of $d$. Coulomb breakup plays negligible role in the breakup of $t$ and ${}^3\mathrm{He}$, in contrast to in the deuteron breakup reaction. It is found that $t$ and ${}^3\mathrm{He}$ tend to break up into three nucleons rather than $d$ and a nucleon.

Conclusions: It is shown that the breakup cross sections of $t$ and ${}^3\mathrm{He}$ are not as large as those of $d$ but non-negligible. Because about 80% of them corresponds to the three-nucleon breakup process, a four-body breakup reaction model is necessary to quantitatively describe the breakup of $t$ and ${}^3\mathrm{He}$.

Figure 1

The Jacobi coordinate for the three-body system. Particles 1, 2, and 3 correspond to $n, n$, and $p$ ($p, p$, and $n$) for $t$ (${}^3\mathrm{He}$), respectively.

Figure 2

Transferred momentum distributions of elastic cross sections of ${}^3\mathrm{He}$ with (a) ${}^{40}\mathrm{Ca}$, (b) ${}^{58}\mathrm{Ni}$, and (c) ${}^{90}\mathrm{Zr}$ targets at 40, 70, and 150 MeV/nucleon. The experimental data are taken from Refs. [20, 21, 22, 23].

Figure 3

(a) Breakup cross section of $t$ with a ${}^{90}\mathrm{Zr}$ target at $E=150$ MeV/nucleon. (b) Same as (a) but of ${}^3\mathrm{He}$.

Figure 4

The energy spectra of breakup cross sections of ${}^3\mathrm{He}$ and $d$ with a ${}^{40}\mathrm{Ca}$ target at (a) 40 MeV/nucleon, (b) 70 MeV/nucleon, and (c) 150 MeV/nucleon. The upper (lower) horizontal axis shows the breakup energy of $d$ (${}^3\mathrm{He}$) regarding the $p+n$ ($p+p+n$) threshold.

Figure 5

Same as in Fig. 4 but with a ${}^{58}\mathrm{Ni}$ target.

Figure 6

Same as in Fig. 4 but with a ${}^{90}\mathrm{Zr}$ target.

Figure 7

Probabilities of the existence of $d$ in the ground and discretized states of ${}^3\mathrm{He}$. The left and right vertical dotted lines represent the thresholds of the $d+p$ and $p+p+n$ channels, respectively.

Figure 8

Total breakup cross sections for ${}^3\mathrm{He}$ breakup reactions separated into the $d+p$ and $p+p+n$ channels by using the $P$-separation method.

Figure 9

Transferred momentum distributions of elastic cross section off ${}^{90}\mathrm{Zr}$. The energies in the panels represent the incident energies per nucleon.

Figure 10

Comparison between the breakup cross sections obtained by four- and three-body E-CDCC with a ${}^{90}\mathrm{Zr}$ target.

Figure 11

The coordinate from c.m. to each particle represented with the Jacobi coordinate. G means the c.m. of the $t$ and ${}^3\mathrm{He}$.