on beta-delayed neutron-emission

We calculated the Q-value of the beta-delayed proton emission in this post. The decay channel is rare, because, when a neutron changes to a proton and emits an electron, the proton orbital must be empty, i.e. the nucleus is N > Z, and the proton emission threshold is larger than neutron threshold. After the beta decay, in most cases, N > Z for the daughter nucleus, so that to have a proton emission is rare.

The situation is different for the beta-delayed neutron emission. After the beta decay, the neutron shell could still have an excessive number of neutrons and undergoes neutron emission. The Q-value for beta-delayed neutron decay is

whenever , the beta-delayed neutron emission is possible. Nuclei with just 2 or 3 neutrons away from the stability village have beta-delayed neutron emission. For example, any isotopes beyond these nuclei can undergo beta-delayed neutron emission ⁹Li, ¹²Be, ¹³B, ¹⁶C, ¹⁷N, ²²O, ²²F, ²⁶Ne, etc.. The 2-step process can be pictured like this:

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The interesting thing about the beta-delayed neutron emission is the nature of the daughter nucleus right after the beta-decay, and the branching ratio for the gamma-decay and neutron emission. Normally, the daughter nucleus is bound and only goes to gamma decay to release excessive energy. When the daughter nucleus is unbound and neutron emission is possible, what is the nature of the nucleus? Since the neutron emission is not 100% but ~15%. This indicates the daughter nucleus is a compound nucleus, involving collective motion.

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In particle configuration, beta decay is when a neutron converts to a proton in the same orbital, as if the neutron decay to proton + electron inside the orbital. For example, 16N beta decay, decays to the 6.14 MeV 3- state (68%) and to the ground state (26%) of 16O. The 3- state can be understood as a coupling of a proton p1/2 hole + a proton d5/2 particle, which can also couple to 8.87 MeV 2- state. The ground state is a sd-shell neutron to proton p1/2. The 7.11 MeV 1- is probably proton p1/2 + a proton s1/2 particle.

Taken from David E. Alburger, Phys. Rev. 111, 1586 (1958)

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17N can populate 17O (Sn = 4.14 MeV ) unbounded state between 4.5 to 6.0 MeV [H. Ohm, W. Rudolph, K.-L. Kratz, Nuclear Physics A 274, 45-52 (1976)]. The 0.0 (5/2+) MeV, 0.87 (1/2+) MeV and 3.06 (1/2-) MeV are also populated by the beta-decay. The ground state can be understood as a sd-shell neutron converting to proton p1/2. The 0.87 MeV state can be imagined as follows, 17N should have a fraction of the sd-shell neutron pair in (s1/2)^2. A s1/2 neutron in 17N converts to proton p1/2 and filled the p-shell, leaving a single s1/2 neutron on top of the 16O core. For the 3.06 MeV state, one of the p1/2 neutrons converts to a proton in the p1/2 orbital, leaving a p1/2 neutron hole in 17O. The spectroscopic factor for the 16O(d,p) reaction of the 3.06 MeV state is only 0.032 and the SF for the same state from 18O(p,d) reaction is 0.88 with L = 1. How to understand the branching ratio? How doe sit related to particle configuration?

Taken from A. R. Poletti and J. G. Pronko, Physical Review C 8, 1285 (1973)

Taken from A. R. Poletti and J. G. Pronko, Physical Review C 8, 1285 (1973)

To be precise, the 4.55 (3/2-), 5.08 (3/2+), 5.39 (3/2-), and 5.93 (1/2-) MeV are populated. These 4 states have been populated by the 16O(d,p) and 18O(p,d) reactions, here are the spectroscopic factors

Energy [MeV]	J-pi	L	SF (adding)	SF (removal)	branching ratio
4.55	3/2-	1	0.23	0.14	36.6 +- 2.6%
5.08	3/2+	2	1.25	0.13	0.6 +- 0.4 %
5.39	3/2-	??	??	??	55.5 +- 3.5%
5.93	1/2-	??	??	??	7.4 +- 0.5%

We can see that, there is 55% to populate 17O 5.39 MeV state, but this state is not known to be populated using a single neutron-adding/removal experiment. It is not clear whether the lack of information is due to experimental limitations or whether those states are not neutron single-particle states. If it is later, the situation becomes very interesting. What is the 5.39 MeV state of 17O?

GEANT4 simulation of HPGe Clover detector

I recently go back to GEANT4 simulation. To simulate the gamma spectrum of the high-purity Germanium (HPGe) Clover detector.

The code is in here: https://github.com/goluckyryan/HPGeClover

Here are some visualizations

The simulated setup for the 16N isomer ration determination. The simulation generate all possible gamma ray energy. We can see a lot of 120 keV gamma being stopped by the vacuum pipe.

The simulation for the 16N isomer decay at the center is like

the simulation caught all feature, but the intensity of the double escape peak from the 6130 keV peak is smaller than the experiment. And the peak to Compton scattering background is different.

Since the strength of the escape peaks are very sensitive to the position and geometry of the crystal, the simulation condition need to be adjusted.

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Here is the program structure. This is also a generic program structure.

comments or to do for the code

• is there a way to get number of clover at EventAction ? I tried to use the G4LogicalVolumeStore, but it seems that the detector is constructed after EventAction.
• is there any way to enable or disable geometry from command ?
• change clover position from command?
• set list of gamma energy and distribution from command
• read file for energy and distribution