Gamma Cascade Transition of 51V(n,g)V52 Reaction

The thermal neutron capture gamma radiations for 51V(n, g)52V reaction have been studied at Dalat Nuclear Research Reactor (DNRR). The gamma two-step cascade transition was measured by event-event coincidence spectrometer. The added-neutron binding energy in 52V was measured as 7.31 MeV. Energy and intensity transition of cascades were consistent with prediction of single particle model. Further more, the spin and parity of levels were confined.

The nuclear data evaluation of 52 V isotope in library was shown the lack of quantum properties of energy levels and the not singular value of spin of some energy levels. The adopted data set looks fairly complete, either missing or being off by about 3%. Energies are probably good to about 0.1 keV. It is hard to assign uncertainties to the intensities, as those of Michaelsen et al. were reported as about 10% but the agreements of the sums into and out off various levels are usually better than 10% [8]. Therefore, the 52 V need to be more experiment information in order to study of nuclear structure. The nucleus 52 V has three protons and one neutron outside a closed shell core having the structure of the doubly magic 48 Ca. It is in a region in which shell model calculations involving coupling between extra-core nucleons in different shell are known to be particularly appropriate [2] [1]. Today, with development of HPGe detector, the sum-coincidence measurement method has been developed to "event-event" coincidence method which is digitalized. In this experiment, the gamma intensities, excited levels of 52 V in energy region below separation neutron energy were measured by "event-event" coincidence method. The experimental results were compared with prediction of single particle model.

Experiment 2.1. The experimental arrangement
The experimental system has been installed at the tangential beam port of the DNRR. The thermal neutron beam was filtered by S, Pb and Si. The neutron flux, the cadmium ratio was 900 (1 cm thinness of cadmium) and the neutron beam at the target position was 1.02 × 10 6 n.cm -2 s -1 . The collimator was made a mixture of paraffin and boron. The distance from the endcap of detectors to the neutron beam center was 4 cm; lead bricks of 10 cm thickness were used to surround the detectors as gamma shields which the background count rate in the 0.2 ÷ 8 MeV range was guaranteed less than 400 counts per second (cps). Two plates of 2 mm thick lead were placed between the detectors and target to decrease the number of backscattered gamma rays and to filter out X-ray.
The electronics configuration was used in those gamma-gamma coincidence experiments are shown in Fig. 1, the parameters of system were setup by method in Ref. [9]. The detector signals are amplified with 572 amplifier (AMP) modules with a shaping time of 3.0 s and about 1 keV/1 channel. Output signals of the amplifiers are digitized by 7072 analog-to-digital converter (ADC) modules. The timing signals of both detectors are put through 474 timing filter amplifier (TFA) modules. The shaped and amplified timing signals by 474 TFA are plugged into 584 CFD modules, which are used in slow rise time rejection option (SRT) mode. The CFD output signal of the first channel (using GPC20 detector) is used as 556 time-to-amplitude converter (TAC) start signal. The CFD output signal of the second channel (using GC2018 detector) is delayed 100 ns and served as a TAC stop signal. The full scale of TAC is set at 500 ns, and output signal is digitized in 8713 ADC with selection of 1024 channels for a 10 V input pulse. The TAC ''Valid Convert'' signal is used to gate 7072 ADC, and the delay for synchronizing with AMP output signal is implemented by interface software. Recorded coincident events have three values, including coincidence gamma-ray energies from detector 1, detector 2 and time interval between two -rays in one detection of pair event.

Fig 1. The electronics configuration.
The target is natural Vanadium which the rich of 51 V is 99.75%, the thermal neutron capture cross section of 51 V is = 4.9 barn [10]. The target was placed between two detectors. Experimental data collected 280 hours total. The coincidence count rate was about 34 cps. The programming interface was set up in event-event coincidence mode. The data on the deposited gamma ray energies and time intervals were recoded and processed off-line by summation of amplitude method.

Data analysis
From the recorded information a set of gamma rays spectra were obtained that belong to all tow step cascades that end at preselected final levels in 52 V. We call these spectra two-step gamma cascades (TSC) spectra and the corresponding TSC final level. Each of these spectra were constructed from deposited energy in one of the detectors under condition that the gamma ray energy sum from both detectors fell within the region of full energy line corresponding to a preselected level. The energies and J of these final levels are listed in Table 1. Note, that in one case two of the levels were not resolved. While constructing the TSC spectra, the background due to accidental coincidences and Compton scattering was subtracted: Compton background was subtracted by choosing background regions on two sides of peak in the spectrum of energy sums; and choosing time windows, selecting three intervals of detection-time difference, was adjusted to isolate the net signal from the background due to accidental coincidences. The constructed TSC spectra were corrected for the energy dependence of the full energy line efficiencies of both detectors. In addition, corrections for the vetoing effects caused by the detection of gamma rays following the decay of the TSC final level and for the effects of gamma-gamma angular correlations were applied. After these corrections the TSC spectra were converted into spectra expressed in absolute TSC intensities. This conversion requires knowledge of the TSC intensity of at least one TSC and it was performed with data from library.
The Fig. 2 is a part of spectrum of gamma ray energy sums accumulated from the event-event mode data obtained from the coincidence neutron capture 51 V. The Fig. 3 is TSC spectrum of 52 V belong to final level at 0 and 18 keV.

Spin assignment and theoretical investigation of the 52 V levels
In neutron capture reaction, if J π is spin of target then J π ± ½ are probability spins of compound nuclear. The emitted gamma rays usually have E1, M1, E2 or M1+E2 called the multi-polarity orders of the radiation. The multi-polarity orders of the radiation are determined: L = 1 is electric dipole (E1) and magnetic dipole (M1), L = 2 is electric quadruple (E2) and magnetic quadruple (M2). The parity will be (-1) L for electric transition, the parity will be (-1) L+1 for magnetic transition [11]. According to the single particle model, the γ-ray transition probability is predicted by Eq. 2 [12].

Parities, spin assignments and transition probabilities
According to the shell model of nucleus, the structure of 51 V is 4 8 4 12 4 8 11 1/2 3/2 1/2 5/2 1/2 3/2 7/2 1s 1p 1p 1d 2s 1d 1f , so the π j of 51 V in ground state is 7/2 -. The π j of the state formed on neutron capture by 51 V may have the value of 3or 4 -(an s-wave neutron can be captured). The π j of 52 V in ground state is 3 + [1] [2][3] [4]. The parity of the 52 V excited state is opposite to the ground state, and the directly gamma emitted compound to ground sate, so transition between these states (transition 1 st order) must be of the E1 type. Further more, refer to the word of Schwager [1], the possibilities π j of 52 V* in intermediate state are 0 + , 1 + , 2 + , 3 + , 4 + , 5 + , 6 + , 7 + , 8 + and 9 + . According to single particle model nuclear structure, applying condition (1), and equation (4), the possibilities spins, parities of levels and transition probabilities of 52 V exciting in thermal neutron capture reaction, are shown in table 3.

Discussion
In this work the final state 17 keV and 22 keV appeared in one peak of the summation spectrum at 18 keV. It is not solved in summation spectrum but in TSC corresponding this peak, the gamma ray energies are separated in two groups, one has summation energies of 7.31 -0.17 MeV and other has summation energy of 7.31 -0.22 MeV.
The neutron binding energy of 52 V appeared in summation spectrum at 7.31 MeV that is consisted with previous research. The spin of gamma ray energies of 356.29 keV, 1002.37 keV, 1307.41 keV, 1358.41 keV, 1634.45 keV and 1664.45 keV are not singular and can be accepted 2 + and 3 + .
The transition probabilities of 52 V are rather consisted with the prediction of single particle model. The difference of experimental and calculation results are about 2 to 22%, it is in range of experiment errors.

Conclusion
In this work, the 36 pairs of gamma two-step cascades were recorded, the results are consisted with prediction of single particle model. The event-event coincidence method is very useful for research of gamma cascade transition which can separated unresolved levels by detectors.