First investigation of hypernuclei in reactions via analysis of emitted bremsstrahlung photons

We investigate possibility of emission of bremsstrahlung photons in nuclear reactions with hypernuclei for the first time. A new model of bremsstrahlung emission which accompanies interactions between $\alpha$ particles and hypernuclei is constructed, where a new formalism for magnetic moments of nucleons and a hyperon inside a hypernucleus is added. To start calculations, we choose $\alpha$ decay of normal nucleus ${}^{210}\mathrm{Po}$ and hypernucleus ${}_{\mathrm{\Lambda }}{}^{211}\mathrm{Po}$. We find that (1) emission for the hypernucleus ${}_{\mathrm{\Lambda }}{}^{211}\mathrm{Po}$ is larger than for the normal nucleus ${}^{210}\mathrm{Po}$ and (2) the difference between these spectra is small. We propose a way to find the hypernuclei where the role of hyperon is the most essential in emission of the bremsstrahlung photons during $\alpha$ decay. As demonstration of such a property, we show that spectra for the hypernuclei ${}_{\mathrm{\Lambda }}{}^{107}\mathrm{Te}$ and ${}_{\mathrm{\Lambda }}{}^{109}\mathrm{Te}$ are essentially larger than the spectra for the normal nuclei ${}^{106}\mathrm{Te}$ and ${}^{108}\mathrm{Te}$. Such a difference is explained by additional contribution of emission to the full bremsstrahlung, which is formed by magnetic moment of hyperon inside hypernucleus. The bremsstrahlung emission formed by such a mechanism is of magnetic type. A new formula for fast estimations of bremsstrahlung spectra for even-even hypernuclei is proposed, where the role of the magnetic moment of the hyperon of the hypernucleus in formation of bremsstrahlung emission is shown explicitly. Then we applied our model to study bremsstrahlung emission in $\alpha$ decay of light hypernuclei ${}_{\mathrm{\Lambda }}{}^{10}\mathrm{Be}$ and ${}_{\mathrm{\Lambda }}{}^{10}\mathrm{B}$ (which was the subject of investigations at the Nuclotron at JINR, Dubna). Such an analysis opens the possibility of new experimental study of properties of the hypernuclei via bremsstrahlung study.

Figure 1

The bremsstrahlung probabilities of photons emitted during $\alpha$ decay of the normal ${}^{210}\mathrm{Po}$ nucleus and the ${}_{\mathrm{\Lambda }}{}^{211}\mathrm{Po}$ hypernucleus in comparison with experimental data (Boie [86, 87]) (parameters of calculations: The bremsstrahlung probability is defined in Eq. (58), and parameters of potentials are taken in Ref. [91]). Here open circles are experimental data [86, 87] for $\alpha$ decay of ${}^{210}\mathrm{Po}$, the blue solid line is the calculated spectrum for $\alpha$ decay of normal nucleus ${}^{210}\mathrm{Po}$ [(a) and (b)], the red dashed line is the calculated spectrum for $\alpha$ decay of hyper nucleus ${}_{\mathrm{\Lambda }}{}^{211}\mathrm{Po}$ with magnetic moments of nucleons and hypeon (a), and the brown dash-dotted line is the calculated spectrum for $\alpha$ decay of hyper nucleus ${}_{\mathrm{\Lambda }}{}^{211}\mathrm{Po}$ without magnetic moments of nucleons and hyperon (b). (a) One can see a small difference between the spectra for the normal and hyper nuclei. Such a difference is explained by the additional contribution of emission of photons formed by the anomalous magnetic moment of a hyperon inside the hyper nucleus ${}_{\mathrm{\Lambda }}{}^{211}\mathrm{Po}$ (which is absent in the normal nucleus ${}^{210}\mathrm{Po}$). (b) Without inclusion of the magnetic moments to calculations, the difference between the spectra for ${}^{210}\mathrm{Po}$ and ${}_{\mathrm{\Lambda }}{}^{211}\mathrm{Po}$ is small also.

Figure 2

The bremsstrahlung probabilities of photons emitted during $\alpha$ decay of the normal nuclei ${}^{106}\mathrm{Te}$ and ${}^{108}\mathrm{Te}$ in comparison with the hypernuclei ${}_{\mathrm{\Lambda }}{}^{107}\mathrm{Te}$ and ${}_{\mathrm{\Lambda }}{}^{109}\mathrm{Te}$ (parameters of calculations: The bremsstrahlung probability is defined in Eqs. (59) and (60); we use $Q=4.290$ MeV for ${}^{106}\mathrm{Te}$ and ${}_{\mathrm{\Lambda }}{}^{107}\mathrm{Te}$, $Q=3.450$ MeV for ${}^{108}\mathrm{Te}$ and ${}_{\mathrm{\Lambda }}{}^{109}\mathrm{Te}$ and $Q$ values for normal nuclei are taken from Table I in Ref. [39]). Here the blue solid line is the calculated spectrum for $\alpha$ decay of normal nucleus ${}^{108}\mathrm{Te}$, the red dashed line is the calculated spectrum for $\alpha$ decay of hypernucleus ${}_{\mathrm{\Lambda }}{}^{109}\mathrm{Te}$ with magnetic moments of nucleons and hyperon, the green dash-dotted line is the calculated spectrum for $\alpha$ decay of normal nucleus ${}^{106}\mathrm{Te}$, and the purple dash-double dotted line is the calculated spectrum for $\alpha$ decay of hypernucleus ${}_{\mathrm{\Lambda }}{}^{107}\mathrm{Te}$ with magnetic moments of nucleons and hyperon. One can see that here the role of the magnetic moment of a hyperon inside a hypernucleus in emission of bremsstrahlung photons is more essential than in previous calculations in Fig. 1 for ${}^{210}\mathrm{Po}$ and ${}_{\mathrm{\Lambda }}{}^{211}\mathrm{Po}$.

Figure 3

The bremsstrahlung probabilities of photons emitted during $\alpha$ decay of the normal nucleus ${}^9\mathrm{Be}$ in comparison with the hypernucleus ${}_{\mathrm{\Lambda }}{}^{10}\mathrm{Be}$ (a) and comparison between the spectra for the normal nucleus ${}^9\mathrm{B}$ and the hypernucleus ${}_{\mathrm{\Lambda }}{}^{10}\mathrm{B}$ (b) (parameters of calculations: The bremsstrahlung probability is defined in Eqs. (59) and (60), $|c_0\left({}_{\mathrm{\Lambda }}{}^{10}\mathrm{B}\right)|=|c_0\left({}_{\mathrm{\Lambda }}{}^{10}\mathrm{Be}\right)|=0.728906$ from Eq. (45), and $E_{\alpha }=8$ MeV basing on analysis in Ref. [92]). Here the blue solid line is the calculated spectrum for $\alpha$ decay of normal nucleus ${}^9\mathrm{Be}$, the red dashed line is the calculated spectrum for $\alpha$ decay of hypernucleus ${}_{\mathrm{\Lambda }}{}^{10}\mathrm{Be}$, the green dash-dotted line is the calculated spectrum for $\alpha$ decay of normal nucleus ${}^9\mathrm{B}$, and the brown dash-double dotted line is the calculated spectrum for $\alpha$ decay of hypernucleus ${}_{\mathrm{\Lambda }}{}^{10}\mathrm{B}$. One can see that difference between these spectra is essentially larger than for the spectra for heavy nuclei and hypernuclei in Figs. 1 and 2. This confirms the essentially more important role of magnetic moment of hyperon inside light hypernucleus in formation of bremsstrahlung emission in comparison with middle and heavy hypernuclei.

Figure 4

The coherent bremsstrahlung cross sections of photons emitted during scattering of $\alpha$ particles off the ${}^{197}\mathrm{Au}$ nuclei in comparison with experimental data at energy of beam of the $\alpha$ particles of 50 MeV. Here black rectangles are experimental data (Sharan 1993: Ref. [101]), the blue solid line is the calculated spectrum in the multipole approach, and the green dash-dotted line is the calculated spectrum in the dipole approach. One can see that the calculated spectra for multipole and dipole approaches have maximums at similar energies of photons (minimums are at different photon energies). This indicates that maximums are not dependent on the method of expansion of the wave function of photons (included to matrix element of emission).