By Andrey V. Davydov

This publication offers the fundamentals and complicated themes of analysis of gamma ray physics. It describes measuring of Fermi surfaces with gamma resonance spectroscopy and the idea of angular distributions of resonantly scattered gamma rays. The dependence of excited-nuclei general lifetime at the form of the exciting-radiation spectrum and electron binding energies within the spectra of scattered gamma rays is defined. Resonant excitation through gamma rays of nuclear isomeric states with lengthy lifetime results in the emission and absorption traces. within the ebook, a brand new gamma spectroscopic process, gravitational gamma spectrometry, is built. It has a solution hundred million occasions larger than the standard Mössbauer spectrometer. one other very important subject of this booklet is resonant scattering of annihilation quanta by means of nuclei with excited states in reference to positron annihilation. the appliance of the equipment defined is to give an explanation for the phenomenon of Coulomb fragmentation of gamma-source molecules and resonant scattering of annihilation quanta to check the form of Fermi surfaces of metals.

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Q1 Þ ð1:67Þ The angular distribution now has the form Wðq1 ; q2 Þ ¼ P mm0 T1 T2 ¼ P ðÀ1ÞÀ2m ð2k1 þ 1Þ1=2 ð2k2 þ 1Þ1=2 k1 k2 N1 N2 mm0 ð1:68Þ From the 3j coefﬁcients appearing in Eq. 68), it follows that N1 = N2 = N. The expression ð2k þ 1Þ1=2 appears as a factor in each term in the ﬁrst brackets [see 1 Eq. 34)]. We represent these brackets as the product ð2k1 þ 1Þ1=2 Uðk1 ; L1 ; L01 ; Ii ; IÞ. 68) the factors I I I I k2 k 1 ð2k1 þ 1Þ and thereupon perform summation m Àm0 ÀN1 m Àm0 ÀN2 / over m and m for them, omitting the phase factor (–1)−2m because 2 m is an integer number that is either even for all values of m or odd for all terms.

5° with the R value obtained upon averaging over all scattering angles allowed by setup geometry—that is, by the dimensions of the gamma source, detector, and working area of the scatterer, as well as by the corresponding distances. 9). 1 keV was measured in many studies. 01) × 10–9 s. 02) × 10–9 s. Although it is quite surprising that the accuracy in determining this quantity became worse in the course of time, either value is acceptable for us. 05) × 10−7 eV. 50) × 107 s–1. 077. 0015) cm/s. 1 keV gamma line in Mössbauer experiments in transmission geometry were performed in several studies quoted in [5, 6, 11–15].

Q1 Þ X I Àm0 & k1 I ÀN1 L01 I L1 k1 Ii ' ð1:66Þ Using Eq. 35); that is, T1 ¼ X ðÀ1Þ IÀm k1 N1 1 =2 I ð2k1 þ 1Þ m I Àm0 k1 fFk1 ðL1 L1 Ii I Þ þ 2dFk1 ðL1 þ 1 L1 Ii I Þ ÀN1 þ d2 Fk1 ðL1 þ 1 L1 þ 1 Ii I ÞgDkN11 0 ðz ! q1 Þ ð1:67Þ The angular distribution now has the form Wðq1 ; q2 Þ ¼ P mm0 T1 T2 ¼ P ðÀ1ÞÀ2m ð2k1 þ 1Þ1=2 ð2k2 þ 1Þ1=2 k1 k2 N1 N2 mm0 ð1:68Þ From the 3j coefﬁcients appearing in Eq. 68), it follows that N1 = N2 = N. The expression ð2k þ 1Þ1=2 appears as a factor in each term in the ﬁrst brackets [see 1 Eq.