Proton emission systematics along proton drip line

Abstract

We analyze the chart containing both spontaneous and beta-delayed proton emission processes in terms of the Coulomb parameter, reduced radius and angular momentum ($χ$, $ρ$, $l$). We then compare the methods to estimate decay width $Γ$ of a resonant state in a proton mean field, namely the continuity equation for outgoing Gamow states, phase shift analysis of real scattering states and numerical integration of the Schrödinger equation in the complex plane. We show that they provide similar results in the region where it is possible to evaluate the imaginary part of the energy for a resonant (Gamow) state. We then investigate the role of the centrifugal barrier induced by Coulomb interaction and also by proton single particle orbitals. We show that the so-called universal decay law, connecting the logarithm of the monopole reduced width to the fragmentation potential, remains also valid for beta-delayed proton emission processes. This fact allows us to describe experimental data for all proton emission processes in terms of a linear dependence connecting the logarithm of the monopole Coulomb-reduced decay width to the logarithm of the monopole Coulomb penetrability and fragmentation potential within a factor of three for absolute values.

Figures (10)

• Figure 1: Fit of the proton experimental spectrum with Lorentzian dependencies in $^{20}$Na.
• Figure 2: Dependence of the reduced radius $\rho$ estimated at the barrier (\ref{['VB']}) versus Coulomb parameter $\chi$. The critical curves corresponding to different angular momenta are solutions of the Coulomb+centrifugal equation (\ref{['crit']}). Circles on the right hand side of the figure correspond to proton emitters with $A>100$Del21, while dark squares on the left hand side correspond to $^{20-21}$Ne and open squares to some representative emitters with known Q-values $^{13}$Al, $^{18}$Ar, $^{30}$Zn, $^{69}$Kr and $^{73}$Sr, taken from Ref. Bat20, as described by Table I.
• Figure 3: Woods-Saxon nuclear+Coulomb+centrifugal potential with universal parametrisation versus radius for $^{21}$Ne corresponding to $l$=0, 1, 2, 3. The horizontal dashed line denotes Q-value.
• Figure 4: Ratio between exact and WKB irregular function $G_l(\chi,\rho)$ versus $\chi/\rho$ for l=0, 1 , 2.
• Figure 5: Logarithm of the monopole Coulomb penetrability $P_0(\chi,\rho)$ versus Coulomb parameter $\chi$ for $\rho$= 1, 2, 3.