Tripathi Formula for "light" Systems

For nuclear-nuclear interactions in which the projectile and/or target are light, Tripathi et al [6] propose an alternative algorithm for determining the interaction cross section (implemented in the new class G4TripathiLightCrossSection). For such systems, Eq.16.4 becomes:

$$\sigma _R = \pi r_0^2 [ A_p^{1/3} + A_t^{1/3} + \delta _E ]^2 (1 - R_C \frac{B}{E_{CM}})X_m$$ (16.5)

$R_C$ is a Coulomb multiplier, which is added since for light systems Eq. 16.4 overestimates the interaction distance, causing $B$ (in Eq. 16.4) to be underestimated. Values for $R_C$ are given in Table 16.2.

$$X_m = 1 - X_1 \exp \left( { - \frac{E}{{X_1 S_L }}} \right)$$ (16.6)

where:

$$X_1 = 2.83 - \left( {3.1 \times 10^{ - 2} } \right)A_T + \left( {1.7 \times 10^{ - 4} } \right)A_T^2$$ (16.7)

except for neutron interactions with $^4$He, for which $X_1$ is better approximated to 5.2, and the function $S_L$ is given by:

$$S_L = 1.2 + 1.6\left[ {1 - \exp \left( { - \frac{E}{{15}}} \right)} \right]$$ (16.8)

For light nuclear-nuclear collisions, a slightly more general expression for $C_E$ is used:

$$C_E = D\left[ {1 - \exp \left( { - \frac{E}{{T_1 }}} \right)... ...E}{{792}}} \right) \cdot \cos \left( {0.229E^{0.453} } \right)$$ (16.9)

$D$ and $T_1$ are dependent on the interaction, and are defined in table 16.3.

Table 16.1: Representative total reaction cross sections

Proj.	Target	Elab	Exp. Results	Sihver	Kox	Shen	Tripathi
		[MeV/n]	[mb]
$^{12}$C	$^{12}$C	30	1316$\pm$40	--	1295.04	1316.07	1269.24
		83	965$\pm$30	--	957.183	969.107	989.96
		200	864$\pm$45	868.571	885.502	893.854	864.56
		300	858$\pm$60	868.571	871.088	878.293	857.414
		870$^1$	939$\pm$50	868.571	852.649	857.683	939.41
		2100$^1$	888$\pm$49	868.571	846.337	850.186	936.205
	$^{27}$Al	30	1748$\pm$85	--	1801.4	1777.75	1701.03
		83	1397$\pm$40	--	1407.64	1386.82	1405.61
		200	1270$\pm$70	1224.95	1323.46	1301.54	1264.26
		300	1220$\pm$85	1224.95	1306.54	1283.95	1257.62
	$^{89}$Y	30	2724$\pm$300	--	2898.61	2725.23	2567.68
		83	2124$\pm$140	--	2478.61	2344.26	2346.54
		200	1885$\pm$120	2156.47	2391.26	2263.77	2206.01
		300	1885$\pm$150	2156.47	2374.17	2247.55	2207.01
$^{16}$O	$^{27}$Al	30	1724$\pm$80	--	1965.85	1935.2	1872.23
	$^{89}$Y	30	2707$\pm$330	--	3148.27	2957.06	2802.48
$^{20}$Ne	$^{27}$Al	30	2113$\pm$100	--	2097.86	2059.4	2016.32
		100	1446$\pm$120	1473.87	1684.01	1658.31	1667.17
		300	1328$\pm$120	1473.87	1611.88	1586.17	1559.16
	$^{108}$Ag	300	2407$\pm$200$^2$	2730.69	3095.18	2939.86	2893.12

1. Data measured by Jaros et al. [5]
2. Natural silver was used in this measurement.

Table 16.2: Coulomb multiplier for light systems [6].

System
p + d	13.5
p + $^3$He	21
p + $^4$He	27
p + Li	2.2
d + d	13.5
d + $^4$He	13.5
d + C	6.0
$^4$He + Ta	0.6
$^4$He + Au	0.6

Table 16.3: Parameters D and T1 for light systems [6].

System	T1 [MeV]	D	G [MeV]
			($^4$He + X only)
p + X	23		(Not applicable)
n + X	18		(Not applicable)
d + X	23		(Not applicable)
$^3$He + X	40	1.55	(Not applicable)
$^4$He + $^4$He	40		300
$^4$He + Be	25	(as for $^4$He + $^4$He)	300
$^4$He + N	40	(as for $^4$He + $^4$He)	500
$^4$He + Al	25	(as for $^4$He + $^4$He)	300
$^4$He + Fe	40	(as for $^4$He + $^4$He)	300
$^4$He + X (general)	40	(as for $^4$He + $^4$He)	75