Momentum peak shift and width of longitudinal momentum distribution of projectilelike fragments produced at $E=290\mathrm{MeV}/\mathrm{nucleon}$

Longitudinal momentum ($P_{\mathrm{L}}$) distributions of projectilelike fragments produced at $E=290\mathrm{MeV}/\mathrm{nucleon}$ are investigated. $P_{\mathrm{L}}$ distributions of fragments produced by Ar and Kr beams with a wide variety of targets (C, Al, Nb, Tb, and Au) were measured using the fragment separator at HIMAC. $P_{\mathrm{L}}$ distributions observed for fragments with a wide range of mass losses $\mathrm{\Delta }A$ (1–30 for Ar beam and 1–64 for Kr beam), show a slightly, but definitely asymmetric nature. The peak shift and width were obtained from the observed $P_{\mathrm{L}}$ distributions. No significant target dependence was found in either the peak shift or width. For the practical application, the variation in momentum peak shift with fragment mass ($A_{\mathrm{F}}$) was represented by a parabolic function. The width on the high-$P_{\mathrm{L}}$ side (${\sigma }_{\mathrm{High}}$) is well reproduced by the Goldhaber formula, which is obtained from the contribution of the Fermi momentum. The behavior of the reduced width, ${\sigma }_0$, obtained from ${\sigma }_{\mathrm{High}}$ via the Goldhaber formulation, is consistent with the mass-dependent Fermi momentum of a nucleon. The width on the low-$P_{\mathrm{L}}$ side (${\sigma }_{\mathrm{Low}}$) is markedly larger than ${\sigma }_{\mathrm{High}}$ and exhibits a clear $A_{\mathrm{F}}$ dependence.

Figure 1

Schematic of secondary beam course SB2.

Figure 2

Particle identification of fragments produced by reactions with (a) an Ar beam and Tb target at $B\rho =5.088\mathrm{Tm}$, and (b) a Kr beam and Tb target at $B\rho =5.462\mathrm{Tm}$.

Figure 3

$P_{\mathrm{L}}$ distributions of fragments produced by Ar beam and Nb target. Arrows indicate momentum of each fragment corresponding to velocity of projectile, ${}^{40}\mathrm{Ar}$, after Nb target. Solid curves represent fits to the asymmetric Gaussian function in Eq. (1).

Figure 4

$P_{\mathrm{L}}$ distributions of fragments produced by Kr beam and Au target. Arrows and solid curves as described in Fig. 3.

Figure 5

TOF distributions of fragments produced through reactions of (a) ${}^{40}\mathrm{Ar}+{}^{159}\mathrm{Tb}$ and (b) ${}^{84}\mathrm{Kr}+{}^{159}\mathrm{Tb}$. Dotted curves represent TOF distributions for projectile. For comparison, the amplitude and peak value for projectile are adjusted to those for fragments.

Figure 6

$P_{\mathrm{L}}$ distributions of fragments produced through few-nucleon removal reactions. The distributions were obtained from TOF data. Arrows and curves as described in Fig. 3.

Figure 7

Momentum shift of fragments produced by Ar beam. Solid lines represent a fit to Eq. (3).

Figure 8

Momentum peak shift of fragments produced by Kr beam. Solid lines represent a fit to Eq. (3).

Figure 9

Momentum peak shift of fragments compared with formulation.

Figure 10

Width of $P_{\mathrm{L}}$ distribution obtained on the high-$P_{\mathrm{L}}$ side with Ar beam. Solid lines show the formulation proposed in Goldhaber [4] with reduced width, ${\sigma }_0=110.2\mathrm{MeV}/c$ [9].

Figure 11

Width of $P_{\mathrm{L}}$ distribution obtained on the high-$P_{\mathrm{L}}$ side with Kr beam. Solid lines as described in Fig. 10. ${\sigma }_0=115.5\mathrm{MeV}/c$ [9] is used for calculation.

Figure 12

Width of $P_{\mathrm{L}}$ distribution obtained on the high-$P_{\mathrm{L}}$ side compared with model calculations. For simplicity, error bars are omitted.

Figure 13

Reduced width for fragments produced by Ar beam. Solid and broken lines indicate, respectively, the average of observed values for each target and the values obtained by the formulation in Ref. [9].

Figure 14

Reduced width for fragments produced by Kr beam. Solid and broken lines as described in Fig. 13.

Figure 15

Energy dependence of reduced width. Solid squares indicate the present results. Other symbols indicate experimental results in Notani [12], Mocko [24], Viyogi [25], and Caamano [26] with Ar beam and those in Bazin [27], Mocko [28], Phaff [8], Stephan [22], and Weber [14] with Kr beam. Solid and broken lines indicate values calculated through the formulas in Refs. [9] and [6].

Figure 16

Reduced width as a function of $A_{\mathrm{P}}$. Solid squares indicate the present results. Other symbols indicate experimental results in Greiner [3], Caamano [26], Mocko [24], Viyogi [25], Stephan [22], and Weber [14]. Broken lines indicate values calculated by the formulas in Ref. [9].

Figure 17

Width of $P_{\mathrm{L}}$ distribution obtained on the low-$P_{\mathrm{L}}$ side for Ar beam. Solid lines as described in Fig. 10. Broken lines indicate values 30% larger than the solid lines.

Figure 18

Width of $P_{\mathrm{L}}$ distribution obtained on the low-$P_{\mathrm{L}}$ side for Kr beam. Solid and broken lines as in Fig. 17.