Laser-nucleus interactions in the sudden regime

The interaction between medium-weight nuclei and a strong zeptosecond laser pulse of MeV photons is investigated theoretically. Multiple absorption of photons competes with nuclear equilibration. We investigate the sudden regime. Here the rate of photon absorption is so strong that there is no time for the nucleus to fully equilibrate after each photon absorption process. We follow the temporal evolution of the system in terms of a set of rate equations. These account for dipole absorption and induced dipole emission, equilibration (modeled in terms of particle-hole states coupled by the residual nuclear interaction), and neutron decay (populating a chain of proton-rich nuclei). Our results are compared with earlier work addressing the adiabatic regime where equilibration is instantaneous. We predict the degree of excitation and the range of nuclei reached by neutron evaporation. These findings are relevant for planning future experiments.

Figure 1

Transitions into class $m$ from neighboring classes $m\pm 1$ described by the nucleon-nucleon interaction matrix element $V_{m^{\prime }m}(i,k)$. Here $F$ represents the Fermi energy and $V$ the threshold energy of the single-particle potential. Particles (blue filled circles) are above $F$; holes (white full circles) are below $F$.

Figure 2

Transitions into class $(i,k,m)$ from neighboring classes $(i,k-1,m-1)$ and $(i,k+1,m+1)$ owing to the laser-nucleus interaction matrix element $W_{k^{\prime }k;m^{\prime }m}\left(i\right)$ with $m^{\prime }=m\pm 1$. See Fig. 1 for further notation.

Figure 3

Transitions into class $(i,k,m)$ from neighboring classes $(i,k-1,m)$ and $(i,k+1,m)$ owing to the laser-nucleus interaction matrix element $W_{k^{\prime }k;mm}\left(i\right)$. See Fig. 1 for further notation.

Figure 4

Density of accessible states ${\rho }_{mm+1}^{\text{acc}}\left(E\right)$ for case (i) (see text) in the constant-spacing model as a function of excitation energy $E$ for $A=42$ particles, 51 single-particle states, $V=45$ MeV, $F=37$ MeV, and $\hslash {\omega }_0=5$ MeV. Colors and symbols correspond to different transitions between particle-hole classes $m\to m+1$.

Figure 5

Density of accessible states ${\rho }_{mm}^{\text{acc}}\left(E\right)$ for case (ii) (see text) in the constant spacing model as a function of excitation energy $E$. We use the same parameters as for Fig. 4. Colors and symbols correspond to transitions within different particle-hole classes $m$.

Figure 6

Contour plots of the time-dependent occupation probabilities $P_m(0,k,t)$ of a light medium-weight nucleus with $A=42$ as a function of excitation energy $E$ for the accessible particle-hole classes. Neutron evaporation is not included. The parameters used are given in the text.

Figure 7

A cut through the contour plots in Fig. 6 at the termination $t=20$ zs of the laser pulse. The occupation probabilities are shown as functions of the number of absorbed photons $k$ for different particle-hole classes.

Figure 8

Contour plot of the time-dependent total occupation probability as a function of excitation energy $E$ and time $t$ for dipole absorption and stimulated emission only (no neutron decay). We use the same parameters as in Fig. 6 (see text).

Figure 9

Level densities ${\rho }_m(0,k)$ for a medium-weight nucleus $A=100$ as functions of excitation energy (measured in units of the number $k$ of absorbed photons). For clarity of illustration we present the densities only for every fourth particle-hole class.

Figure 10

Contour plots of the time-dependent occupation probabilities $P_m(0,k,t)$ for every second accessible particle-hole class from $1\mathrm{p}\text{−}1\mathrm{h}$ to $47\mathrm{p}\text{−}47\mathrm{h}$ as functions of excitation energy $E$ for dipole absorption and stimulated emission only (no neutron emission). The parameters are mass number $A=100$, the single-particle level density as given in Eq. (10), ${\tilde{\mathrm{\Gamma }}}_{\mathrm{dip}}=20$ MeV, and $\tau =40$ zs.

Figure 11

Contour plots of the time-dependent total occupation probabilities $P(0,k,t)$. (a) Photon absorption or emission allows for the two possible processes presented in Figs. 2 and 3. (b) Photon absorption or emission allows only for the process in Fig. 2. The parameters are the same as in Fig. 10.

Figure 12

Contour plots of the total time-dependent occupation probabilities $P(0,k,t)$ versus time $t$ and excitation energy $E$ for four values of ${\tilde{\mathrm{\Gamma }}}_{\mathrm{dip}}$ as indicated. The other parameters are the same as in Fig. 10.

Figure 13

Total excitation energy $E_{\mathrm{tot}}$ (solid lines, left vertical axis) and approximate time interval between two photon absorptions ${\mathrm{\Delta }}_{1}t$ (dashed lines, right vertical axis) as a function of time for ${\tilde{\mathrm{\Gamma }}}_{\mathrm{dip}}=5$ MeV (blue circles) and ${\tilde{\mathrm{\Gamma }}}_{\mathrm{dip}}=20$ MeV (red squares). The inset zooms in the interval of the first 10 zs for ${\mathrm{\Delta }}_{1}t$.

Figure 14

Total occupation probabilities (solid lines) compared with results from Ref. [26] for the quasiadiabatic regime (dashed lines) as a function of the number $k$ of absorbed photons at times $t=$ 2, 10, 40, and 100 zs and for ${\tilde{\mathrm{\Gamma }}}_{\mathrm{dip}}=5$ MeV.

Figure 15

Relative difference $R_m\left(k\right)=2[P_m^{\mathrm{eq}}(0,k,t)-P_m(0,k,t)]/[P_m^{\mathrm{eq}}(0,k,t)+P_m(0,k,t)]$ as a function of excitation energy $E$ and particle-hole class $m$. We consider snapshots at $t=5,10$, and 20 zs for effective dipole absorption rates ${\tilde{\mathrm{\Gamma }}}_{\mathrm{dip}}=5$ MeV and 20 MeV. The dashed line shows the function $E\left(m\right)=m\hslash {\omega }_0$ with $\hslash {\omega }_0=5$ MeV. See text for further explanations.

Figure 16

Comparison of total occupation probabilities for target nucleus ($i=0$) summed over all particle-hole classes as a function of the number $k$ of absorbed photons at times $t=$ 2, 4, 6, and 8 zs. We calculate the neutron decay rates considering only $m^{\prime }=m$ (dashed lines) or only $m^{\prime }=m-1$ (solid lines). We use ${\tilde{\mathrm{\Gamma }}}_{\mathrm{dip}}=5$ MeV.

Figure 17

Contour plots of the time-dependent occupation probabilities summed over all particle-hole classes as a function of excitation energy $E$ for target nucleus ($i=0$) and three generations of daughter nuclei ($i=1,2,3$). The parameters are the mass number $A=100$, Eq. (10) for the single-particle level density, ${\tilde{\mathrm{\Gamma }}}_{\mathrm{dip}}=5$ MeV, $\tau =20$ zs, and $\hslash {\omega }_0=5$ MeV.

Figure 18

The same as in Fig. 17 for ${\tilde{\mathrm{\Gamma }}}_{\mathrm{dip}}=20$ MeV.