Primary $\gamma$-ray spectra in ${}^{44}$Ti of astrophysical interest

Primary $\gamma$-ray spectra for a wide excitation-energy range have been extracted for ${}^{44}$Ti from particle-$\gamma$ coincidence data of the ${}^{46}$Ti($p,t\gamma$)${}^{44}$Ti reaction. These spectra reveal information on the $\gamma$-decay pattern of the nucleus and may be used to extract the level density and radiative strength function applying the Oslo method. Models of the level density and radiative strength function are used as input for cross-section calculations of the ${}^{40}$Ca($\alpha ,\gamma$)${}^{44}$Ti reaction. Acceptable models should reproduce data on the ${}^{40}$Ca($\alpha ,\gamma$)${}^{44}$Ti reaction cross section as well as the measured primary $\gamma$-ray spectra. This is only achieved when a coherent normalization of the slope of the level density and radiative strength function is performed. Thus, the overall shape of the experimental primary $\gamma$-ray spectra puts a constraint on the input models for the rate calculations.

Figure 1

Identification of particle species using the $\Delta E-E$ technique.

Figure 2

Singles (blue) and coincidence (red) triton spectra. The impurities of ${}^{48,50}$Ti are easily seen. The resolution is $\approx$$270–330$ keV.

Figure 3

The first-generation spectra for each excitation-energy bin in ${}^{44}$Ti. The dashed lines are limits set for the further analysis (see text).

Figure 4

Original (a), unfolded (b), and first-generation (c) $\gamma$-ray spectrum of ${}^{44}$Ti for excitation energy $E=6.1$ MeV.

Figure 5

Comparison of experimental primary $\gamma$-ray spectra (solid squares) and the ones obtained from multiplying the extracted $\rho$ and $\mathcal{T}$ functions (red line) for several excitation energies. The experimental and calculated spectra are shown for excitation-energy bins of 467 keV.

Figure 6

Experimental data points (solid squares) normalized to the CT model (dashed line) and data points (blue, open circles) normalized to the calculation of GHK (dash-dotted line). The black, solid line represents the known levels taken from Ref. [25].

Figure 7

Experimental average radiative width (solid squares) for ${}^{47–51}$Ti as a function of neutron separation energy and estimated width for ${}^{44}$Ti (open square).

Figure 8

Normalized RSFs for the two normalizations of the level density. The dashed line is the upper limit for the CT normalization, while the dash-dotted line is the lower limit for the GHK normalization.

Figure 9

Radiative strength functions and fitted models for (a) the CT and (b) the GHK normalization. Note that the SLO model has not been fitted to the data.

Figure 10

Radiative strength functions extracted for two different excitation-energy regions as compared to the one from the total excitation-energy region under consideration (all cases are normalized to the CT level density). The standard GLO model is also shown for these ranges of excitation energy and the extreme cases $T_f=0$ and $E=9.9$ MeV.

Figure 11

Experimental primary $\gamma$ spectra (solid squares) and those obtained from multiplying the extracted $\rho$ and $\mathcal{T}$ functions (red line) for $4.6⩽E⩽7.0$ MeV. These are compared with calculated spectra using the six inputs as described in the text. The experimental and calculated spectra are given for excitation-energy bins of 466.8 keV.

Figure 12

Same as Fig. 11 for $7.4⩽E⩽9.8$ MeV.

Figure 13

(a) Data on the Maxwellian-averaged reaction rate for the ${}^{40}$Ca($\alpha ,\gamma$) reaction from Ref. [1] are compared to calculations with inputs 1, 2, 7, and 8. (b) Ratio of the calculated reaction rates and experimental data. The upper dotted line indicates a 40% deviation from the experimental data, while the lower dotted line indicates a 20% deviation.