Laser-nucleus interactions: The quasi-adiabatic regime

The interaction between nuclei and a strong zeptosecond laser pulse with coherent MeV photons is investigated theoretically. We provide a first semiquantitative study of the quasi-adiabatic regime where the photon absorption rate is comparable to the nuclear equilibration rate. In that regime, multiple photon absorption leads to the formation of a compound nucleus in the so-far unexplored regime of excitation energies several hundred MeV above the yrast line. The temporal dynamics of the process is investigated by means of a set of master equations that account for dipole absorption, stimulated dipole emission, neutron decay, and induced fission in a chain of nuclei. That set is solved numerically by means of state-of-the-art matrix exponential methods also used in nuclear fuel burn-up and radioactivity transport calculations. Our quantitative estimates predict the excitation path and range of nuclei reached by neutron decay and provide relevant information for the layout of future experiments.

Figure 1

Distribution of total spin values of the compound nucleus for several values of the number $N_0$ of absorbed photons.

Figure 2

Widths for effective dipole absorption (solid red line), stimulated dipole emission (long-dashed green line) (both for $N{\mathrm{\Gamma }}_{\mathrm{dip}}=5$ MeV), band for neutron emission (short-dashed dark blue lines), and band for induced fission (dashed-dotted light blue lines) versus excitation energy $E$ for $A=100$ (148 bound single-particle states). The two neutron decay widths are calculated from the Weisskopf estimate $\left[T\right(E)=1]$ and by taking for the transmission coefficients uniformly the value $T\left(E\right)=1/2$. The two fission widths are obtained using the values $\hslash {\omega }_1=2$ and 4 MeV.

Figure 3

Same widths as in Fig. 2 for $A=200$ (360 bound single-particle states).

Figure 4

Occupation probabilities $P(0,E,t)$ for $E_L=5$ MeV, $A=100$, and for dipole absorption and stimulated emission only. (a)–(c) Contour plots of the time-dependent occupation probability $P(0,E,t)$ as a function of excitation energy $E$ for (a) $N{\mathrm{\Gamma }}_{\mathrm{dip}}=1$ MeV, (b) $N{\mathrm{\Gamma }}_{\mathrm{dip}}=5$ MeV, and (c) $N{\mathrm{\Gamma }}_{\mathrm{dip}}=8$ MeV. (d)–(f) Corresponding peak height (dashed blue line) (scale on the right $y$ axis), position (solid red line), and FWHM (long-dashed green line) of the occupation probability (scales on the left $y$ axis) for (d) $N{\mathrm{\Gamma }}_{\mathrm{dip}}=1$ MeV, (e) $N{\mathrm{\Gamma }}_{\mathrm{dip}}=5$ MeV, and (f) $N{\mathrm{\Gamma }}_{\mathrm{dip}}=8$ MeV.

Figure 5

Occupation probabilities $P(0,E,t)$ for $E_L=5$ MeV, $A=200$, and for dipole absorption and stimulated emission only. (a)–(c) Contour plots of the time-dependent occupation probability $P(0,E,t)$ as a function of excitation energy $E$ for (a) $N{\mathrm{\Gamma }}_{\mathrm{dip}}=1$ MeV, (b) $N{\mathrm{\Gamma }}_{\mathrm{dip}}=5$ MeV, and (c) $N{\mathrm{\Gamma }}_{\mathrm{dip}}=8$ MeV. (d)–(f) Corresponding peak height (dashed blue line) (scale on the right $y$ axis), position (solid red line), and FWHM (long-dashed green line) (scales on the left $y$ axis) of the occupation probability and for (d) $N{\mathrm{\Gamma }}_{\mathrm{dip}}=1$ MeV, (e) $N{\mathrm{\Gamma }}_{\mathrm{dip}}=5$ MeV, and (f) $N{\mathrm{\Gamma }}_{\mathrm{dip}}=8$ MeV.

Figure 6

Contour plots of the time-dependent occupation probability $P(0,E,t)$ as a function of excitation energy $E$ for (a) $E_L=1$ MeV, (b) $E_L=5$ MeV, and (c) $E_L=10$ MeV. The results are for $N{\mathrm{\Gamma }}_{\mathrm{dip}}=5$ MeV, $A=100$, and for dipole absorption and stimulated emission only.

Figure 7

Contour plots of the time-dependent occupation probabilities $P(i,E,t)$ with (from top to bottom) target nucleus ($i=0$, label $T$) and four daughter nuclei ($i=1$ to 4, labels $D1–D4$) as functions of excitation energy $E$ for $N{\mathrm{\Gamma }}_{\mathrm{dip}}=5$ MeV. Left column: target nucleus $A=100$, photon energy $E_L=5$ MeV; middle column: target nucleus $A=100$, photon energy $E_L$ = 10 MeV; right column: target nucleus $A=200$, photon energy $E_L$ = 5 MeV. Please note the different color coding span for the case with target nucleus $A=200$, which we chose for purpose of comparison with the next figure.

Figure 8

Same as Fig. 7 but including induced fission.

Figure 9

Loss of total occupation probability ${\sum }_{i,k}P(i,k,t)$ due to fission for the three parameter sets used in Figs. 7 and 8: $N{\mathrm{\Gamma }}_{\mathrm{dip}}=5$ MeV in all cases, (i) target nucleus with $A=100$, photon energy $E_L=5$ MeV (solid red line), (ii) target nucleus with $A=100$, photon energy $E_L=10$ MeV (long-dashed green line), and (iii) target nucleus with $A=200$, photon energy $E_L=5$ MeV (short-dashed blue line).