# Beta-Delayed Neutron Emission

## Introduction

Close to the line of nuclear stability, beta decay leaves the daughter in a neutron bound state. De-excitation proceeds via the emission of characteristic gamma rays. This does not hold true as one considers exotic nuclei. The nuclear structure changes as nuclei become more neutron rich. The proton / neutron imbalance in the orbitals cause a shift nuclear energetics. The shift manifests itself as a decrease in the neutron separation energy.

As the separation energy decreases, the beta-decay daughter gains extra decay channels. More decay channels open up as the Q-value becomes larger. The final state may have an excitation energy greater than the neutron separation energy ($S_n$). When this occurs, we observe an increased possibility of neutron emission. McMillan and others discovered this decay mode in 1939[efn_note]McMillan, E.; Radioactive Recoils from Uranium Activated by Neutrons; Phys. Rev., 1939, Vol. 55, pp. 510 [/efn_note]. Since then, it has become a critical tool to study nuclear structure.

Schematically, one may view this process as shown in the figure to the right. The first panel shows the beta strength distribution ($S _\beta$). This represents the matrix elements of the decay. The second panel shows the Fermi integral. This integral enhances decays to low energy states. Combine the first two panels, and we get the intensities ($I_\beta$) of the daughter states. Remember, from our introduction, that we use this information to determine nuclear lifetimes.

Experimentally, we work backwards from $I_\beta$ to $S_\beta$. For states below $S_n$, we use traditional gamma spectroscopy. Above $S_n$, we use beta-delayed neutron spectroscopy. Combining these two measurements, yields a complete picture of $S_\beta$.

## Experimental Work

Beta-delayed neutron emission from fission fragments provides theorists and experimentalists plenty of work. The fission of 235U produces isotopes for study. In the past, 3He and CH4 ionization chambers measured neutron energy spectra. Both detector types offer energy excellent energy resolution. This, coupled with new separation techniques, provided interesting new neutron energy spectra. Surprisingly, the spectra displayed discrete lines. The lines suggest well-defined neutron emitting daughter states[efn_note] Rudstam, G., Shalev, S. and Jonsson, O.; Delayed neutron emission from separated fission products; NIM, 1974, Vol. 120(2), pp. 333-344 [/efn_note],[efn_note] Kratz, K. L., et al. Investigation of Beta strength functions by neutron and gamma-ray spectroscopy; Nucl. Phys. A, 1979, Vol. 317, pp. 335-362[/efn_note].

## Theoretical Work

Hardy challenged this interpretation, and proposed the Pandemonium effect[efn_note] Hardy, J., Carraz, L., Jonson, B. and Hansen, P.; The essential decay of pandemonium: A demonstration of errors in complex beta-decay schemes; Phys. Lett. B, 1977, Vol. 71(2), pp. 307-310 [/efn_note],[efn_note] Hardy, J. C., Jonson, B. and Hansen, P. G.The essential decay of pandemonium: β-delayed neutrons; Nucl. Phys. A, 1978, Vol. 305, pp. 15-28 [/efn_note]. Pandemonium is a fictional nucleus. It demonstrates structures observed in particle emission spectra arise from statistical fluctuations. These fluctuations are due to high level densities in the beta-decay daughter. Pandemonium’s neutron emission spectra are similar to those studied by Kratz et al. While the spectra are not identical, the gross structure of the spectra agrees quite well. This leads Hardy et al. to suggest beta-delayed neutron spectra interpretation is not trivial. Any interpretation of these data must consider pandemonium.

More recent theoretical work combines QRPA Hauser-Feschbach statistical models[efn_note] Hauser, W. and Feshbach, H.; The Inelastic Scattering of Neutrons; Phys. Rev., American Physical Society, 1952, Vol. 87, pp. 366-373 [/efn_note],[efn_note] Kawano, T., Möller, P. and Wilson, W. B.; Calculation of delayed-neutron energy spectra in a quasiparticle random-phase approximation-Hauser-Feshbach model; Phys. Rev. C, 2008, Vol. 78, pp. 054601 [/efn_note]. QRPA calculates the beta-decay probabilities of states in the daughter nucleus. These states decay either via gammas or neutrons. The Hauser-Feschbach model calculates the branching ratios. This framework considers both nuclear structure effects and statistical effects. It does this by accounting for spin and parity selection rules. Overall, it predicts the correct neutron energy range in the decay. The deficiency is that it does not reproduce discrete peaks in the spectra.

## Declining interest

In the mid to late 1990s, interest in beta-delayed neutron emission waned. Researchers hit technical challenges in radioactive ion beam production. They couldn’t produce the exotic nuclei in the required purities or rates. Detectors lacked the efficiency required to measure at available rates. To make matters worse, Pandemonium reared its head. Many measurements
displayed the tell-tale signs of being statistical in nature. With a few exceptions[efn_note] Greenwood, R. C. and Watts, K. D.; Delayed Neutron Energy Spectra of 87Br, 88Br, 89Br, 90Br, 137I, 138I, 139I,136Te; Nucl. Sci. Eng., 1997, Vol. 126, pp. 324-332 [/efn_note],[efn_note] Perru, O., et al.; Decay of neutron-rich Ga isotopes near N = 50 at PARRNe; Phys. At. Nucl., Nauka/Interperiodica, 2003, Vol. 66(8), pp. 1421-1427 [/efn_note], researchers began studying neutrons from transfer reactions or other sources.

## Conclusions

It may sound like we’re ending on a sour note. Yes, and no. It’s unfortunate that researchers couldn’t continue such exciting work. But, it’s good that they didn’t. It gave this author a shot at a degree, doing some cool work.