⁷Li(p,γ) measurement

Motivation

The ⁷Be(n,α)⁴He cross section measured at n_TOF [1] provided a new reaction rate for BBN calculations. However, the total rate for this reaction had to be determined by a combination of experimental data and theoretical estimate. In particular, the n_TOF data provided effectively a fraction of the total rate, i.e. the fraction corresponding to the (n,γα) channel, proceeding through a γ-ray transition to the doublet 2⁺ excited states in ⁸Be, which then decay by the emission of 2α's. This, according to the calculations presented in [1] and in the corresponding supplementary material, corresponds to approximately 3.2% of the total rate. In fact, the contribution from transitions to all other bound levels in ⁸Be could not be determined directly in that measurement.

It is possible, however, to access all the γ-ray transitions leading to the relevant states in ⁸Be also from the ⁷Li(p,γ) channel. Therefore, a measurement of the partial transition strengths (Γ_γ's) could provide a full and consistent picture for the (n,α) rate.

The ⁷Li(p,γ)⁸Be, Q = 18.899 MeV and no threshold, can proceed through emission of a few discrete γ-rays, according to the following scheme:

In the figure, γ-rays from the J^π=2^- state, which is located just above the ⁷Be(p,n) threshold, are indicated, because the main contribution to the capture cross section is supposed to be coming from this state. However, transitions from the J^π=1^- state at 19.4 MeV are included as well in the calculations (see below).

Calculations of the cross section have been performed using the experimental information available for the transitions to the higher J^π=2⁺ doublet in ⁸Be at ~ 16 MeV, obtained with the (n,γα) measurement performed at n_TOF [1]

Both, a direct capture mechanism (DRC) and the single-level Breit-Wigner (SLBW) processes are possible for the capture reaction process. In the case of the SLBW calculation, the partial Γ_γ are fixed to reproduce the measured cross section of the (n,γα) reaction.

initial state	Ex [MeV]	Total width [keV]	Ep(CM) [MeV]	final state	Eγ [MeV]	Γγ [eV] (adopted)	Γγ [eV] (experimental)
2-	18.91	122	1.656	0+1	18.91	0.0	-
				2+1	15.88	4.41	-
				2+2 & 2+3	2.28 - 1.99	0.3	0.27 ± 0.08
1-	19.40	~645	2.146	0+1	19.40	12.4	-
				2+1	16.37	9.5	-
				2+2 & 2+3	2.77 - 2.48	0.7	-

The partial widths to the ground state and to the first excited state in ⁸Be have been deduced from DRC calculations, fixed to reproduce the experimental (n,γα) cross section shown above. It is important to note that the n_TOF measured cross section is in very good agreement with the SLBW calculation obtained with the only experimental measured partial width, if an additional contribution from the 1^- state is included.

Partial (p,γ) cross section estimate

The results of the calculation of the partial capture cross sections for transitions leading to the ground state, first excited and third and fourth excited states in ⁸Be are shown here below for both DRC and SLBW reaction models, for incident proton energies ranging from 1 to 5 MeV.

Event rate

With a beam current of I_p=0.5 μA for protons of 1 - 5 MeV energy, the event rate can estimated for a Li target similar to that used in the measurement of C Lederer et al. [2]. Other parameters are as follows

#Li target              :  disk
#molecular mass   [amu] :  0.70000E+01
#diameter          [cm] :  0.25000E+01
#area             [cm2] :  0.49087E+01
#mass               [g] :  0.27690E-02
#number of atoms        :  0.23822E+21
#areal density [atom/b] :  0.48530E-04
#volume           [cm3] :  0.49087E-02
#thickness         [cm] :  0.10000E-02
#density        [g/cm3] :  0.56410E+00
#               [1/cm3] :  0.48530E+23
  
#cross section      [b] :  0.10000E-05
#flux (p/sarea) [1/cm2] :  0.63560E+12
#number of reactions    :  0.15141E+03

For a cross section of 1 μb, one could expected about 150 γ-ray/sec emitted at 4π.

References

1. M Barbagalllo et al. (The n_TOF Collaboration), Be-7(n,α)He-4 Reaction and the Cosmological Lithium Problem: Measurement of the Cross Section in a Wide Energy Range at n_TOF at CERN, Phys. Rev. Lett. 117, 152701 (2016). doi
2. Lederer, C., Käppeler, F., Mosconi, M., Nolte, R., Heil, M., Reifarth, R., Schmidt, S., Dillmann, I., Giesen, U., Mengoni, A., Wallner, A., Definition of a standard neutron field with the Li-7(p,n)Be-7 reaction , Physical Review C 85, 055809 (2012). doi

-- AlbertoMengoni - 2018-04-28