Theoretical Conversion Coefficients Research Articles

On the graphical extraction of multipole mixing ratios of nuclear transitions

We propose a novel graphical method for determining the mixing ratios δ and their associated uncertainties for mixed nuclear transitions. It incorporates the uncertainties on both the measured and the theoretical conversion coefficients. The accuracy of the method has been studied by deriving the corresponding probability density function. The domains of applicability of the method are carefully defined.

High-resolutionαand electron spectroscopy ofCf98249

$\ensuremath{\alpha}$-particle spectra of $^{249}\mathrm{Cf}$ have been measured with a double-focusing magnetic spectrometer and with passivated implanted planar silicon (PIPS) detectors. The conversion-electron spectra of $^{249}\mathrm{Cf}$ have been measured with a cooled Si(Li) detector and with a room-temperature PIPS detector. Precise energies of $\ensuremath{\alpha}$ groups in the decay of $^{249}\mathrm{Cf}$ have been measured with respect to the known energy of $^{250}\mathrm{Cf}$. In addition, $\ensuremath{\alpha}$-electron, $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\gamma}$, and $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence measurements were also performed to determine the spin-parity of the previously known 643.64-keV level. From electron intensities, conversion coefficients of transitions in the daughter $^{245}\mathrm{Cm}$ have been determined. The measured ${L}_{3}$ conversion coefficients of the 333.4- and 388.2-keV transitions are found to be in agreement with the theoretical conversion coefficients for pure $E1$ multipolarity. On the other hand, the $K,{L}_{1}+{L}_{2},M$, and $N$ conversion coefficients are approximately twice the theoretical values for pure $E1$ transitions. These measurements indicate anomalous $E1$ conversion coefficients for the 333.4- and 388.2-keV transitions, as has been pointed out in earlier measurements. The measured conversion coefficient of the 255.5-keV transition gives an $M1$ multipolarity for this transition which establishes a spin-parity of 7/${2}^{\ensuremath{-}}$ and the 7/${2}^{\ensuremath{-}}[743]$ single-particle assignment to the 643.64-keV level.

Conversion coefficients for superheavy elements

In this paper, we report on internal conversion coefficients for Z=111 to Z=126 superheavy elements obtained from relativistic Dirac–Fock calculations. The effect of the atomic vacancy created during the conversion process has been taken into account using the so called “Frozen Orbital” approximation. The selection of this atomic model is supported by our recent comparison of experimental and theoretical conversion coefficients across a wide range of nuclei. The atomic masses, valence shell electron configurations, and theoretical atomic binding energies required for the calculations were adopted from a critical evaluation of the published data. The new conversion coefficient data tables presented here cover all atomic shells, transition energies from 1 keV up to 6000 keV, and multipole orders of 1–5. A similar approach was used in our previous calculations [T. Kibédi, T.W. Burrows, M.B. Trzhaskovskaya, P.M. Davidson, C.W. Nestor Jr., Nucl. Instrum. Methods Phys. Res. A 589 (2008) 202] for Z=5–110.

Conversion Coefficients for Superheavy Elements

In this paper, we report on internal conversion coefficients for Z = 111 to Z = 126 superheavy elements obtained from relativistic Dirac–Fock calculations. The effect of the atomic vacancy created during the conversion process has been taken into account using the so called ‘‘Frozen Orbital’’ approximation. The selection of this atomic model is supported by our recent comparison of experimental and theoretical conversion coefficients across a wide range of nuclei. The atomic masses, valence shell electron configurations, and theoretical atomic binding energies required for the calculations were adopted from a critical evaluation of the published data. The new conversion coefficient data tables presented here cover all atomic shells, transition energies from 1 keV up to 6000 keV, and multipole orders of 1–5. A similar approach was used in our previous calculations [T. Kibedi, T.W. Burrows, M.B. Trzhaskovskaya, P.M. Davidson, C.W. Nestor Jr., Nucl. Instrum. Methods Phys. Res. A 589 (2008) 202] for Z = 5–110.

Evaluation of theoretical conversion coefficients using BrIcc

A new internal conversion coefficient database, BrIcc has been developed which integrates a number of tabulations on internal conversion electron (ICC) and electron–positron pair conversion coefficients (IPC), as well as Ω(E0) electronic factors. A critical review of general formulae and procedures to evaluate theoretical ICC and IPC values are presented, including the treatment of uncertainties in transition energy and mixing ratio in accordance with the Evaluated Nuclear Structure Data File. The default ICC table, based on the Dirac–Fock calculations using the so called “Frozen Orbital” approximation, takes into account the effect of atomic vacancies created in the conversion process. The table has been calculated for all atomic shells and to cover transition energies of 1–6000keV and atomic numbers of Z=5–110. The software tools presented here are well suited for basic nuclear structure research and for a range of applications.

Positron spectra from internal pair conversion observed in 238U + 181Ta collisions

We present new results from measurements and simulations of positron spectra, originating from 238U + 181Ta collisions at beam energies close to the Coulomb barrier. The measurements were performed using an improved experimental setup at the double-Orange spectrometer of GSI. Particular emphasis is put on the signature of positrons from Internal-Pair-Conversion (IPC) processes in the measured e+ energy spectra, following the de-excitation of electromagnetic transitions in the moving Ta-like nucleus. It is shown by Monte Carlo simulations that, for the chosen current sweeping procedure used in the present experiments, positron emission from discrete IPC transitions can lead to rather narrow line structures in the measured energy spectra. The measured positron spectra do not show evidence for line structures within the statistical accuracy achieved, although expected from the intensities of the observed $\gamma$ transitions (E$_{\gamma}~1250-1600$ keV) and theoretical conversion coefficients. This is due to the reduced detection efficiency for IPC positrons, caused by the limited spatial and momentum acceptance of the spectrometer. A comparison with previous results, in which lines have been observed, is presented and the implications are discussed.

Nuclear Data Sheets for A = 163

Nuclear structure data for all nuclei with mass number A=163 have been evaluated. Adopted values for level properties and detailed level and decay schemes are presented for each nucleus, along with the experimental data upon which they are based. Theoretical (Hager-Seltzer) conversion coefficients for pure multipole transitions are presented without uncertainties. For mixed transitions, the stated conversion-coefficient uncertainties take into account the uncertainty of the mixing ratio as well as the uncertainties of the theoretical conversion coefficients for the pure multipole components (2% for M1, E2, and E1 transitions and 5% for all others).

Nuclear Data Sheets for A = 150

Nuclear Data Sheets for A=150 (last compiled in 1964) have been prepared using all pertinent experimental information from more than 300 papers (received prior to March 1975). Some information is now available for 11 elements, from Ce through Er. This mass chain is of particular interest since it lies in a region of transition from spherical to deformed nuclei; sufficient J π-information is available for Sm to enable a meaningful comparison of its low-lying bands of levels with those of nearby nuclei. Less extensive level schemes now exist for Gd (about 40 levels, 7 firm J π-assignments) and Nd (10 levels, 3 firm J π-assignments). The 4 states postulated on the basis of γ-cascades in each of Ce and Dy require verification. In the odd-mass A=150 nuclei (Pr, Pm, Eu, Tb, Ho) only one excited state has been identified (in Tb) apart from isomeric states. Isomers exist for Eu, Tb and possibly Ho, but the excitation energy is unknown in each case so it is not clear which long-lived state is the ground state, although most authors assume low-spin Eu and Tb to represent the ground state. Spin measurements for Pr, Pm, Tb and Ho ground states and Eu and Tb isomeric states are needed since shell-model systematics do not give reliable predictions in this mass region and (β + + ε)-decay does not generate definite assignments. T ½ ≈ 34 y is now adopted for high-spin Eu, and the possible existence of a third long-lived state of Eu (to explain earlier data giving T ½ ≈ 6 y for the former state) is presently under investigation by J. Mihelich. The adopted value of Q + for 3-h Tb (based on experimental E β ) disagrees with the value in the current mass table, presumably because the latter assumes that 3-h Tb (J=2?) a-decay populates the 4 − ground state of 146Eu. Despite the volume of Sm(n, γ) data available, the majority of transitions remain unplaced, and a number of unresolved doublets presumably persist. [Extensive, Ge(Li) detector coincidence data would probably resolve many existing ambiguities.] Separate experiments yield inconsistent intensities for a number of weak ce-lines. Because of space limitations, theoretical conversion coefficients used to deduce multipolarities for Sm and Gd transitions are not shown but are available from the authors upon request. Note that 3-h Tb, 34-y Eu, and 40-s Ho decay schemes and much of the Nd level scheme are based on presently unpublished data. The following is a partial list of papers pertaining to A=150 nuclei, but containing no new experimental data for those nuclei: Ce: 71Ge15, 72Wi15, 73Fl02; Dy: 60To05, 64Ma17; Eu: 60To05; Gd: 60To05, 72Hs07; Nd: 65So04, 70Se18, 70Va22, 72Ab18, 72Br61, 72Ru08, 73Ab06, 73Gu09, 73Le19, 73Me05, 73Me08, 73Pr14, 73Pr19, 73To15, 74Ca05, 74En08; Pm: 60To05; Sm: 65Le23, 68Lu12, 69Ca02, 70Be72, 70Ra28, 70Ru05, 70Sc35, 70Se18, 70So02, 71Be95, 71Dz04, 71Ku32, 71Ta27, 72BaC7, 72BeA2, 72Ko58, 72Ma17, 72Wi15, 73Bu30, 73Gu09, 73Pe15, 73Pr14, 73Sa14, 73Si25, 74Ca05, 74Ja13, 74Kr16, 74Ku14, 74Le26; Tb: 60To05, 72Ar36.

Internal conversion of high-multipolarity transitions in109Ag and113In

The internal conversion coefficients were measured for the 88.032 keVE3 transition in109Ag using the 4π pressurized proportional counter, the windowless 4π scintillation counter and the double-focusing magnetic spectrometer. The results are:α T =26.4±0.4,α K =11.4±0.3,\(\alpha _{L_1 } = 0.63 \pm 0.13, \alpha _{L_2 } = 5.48 \pm 0.18, \alpha _{L_3 } = 6.11 \pm 0.20, \alpha _M = 2.40 \pm 0.08, \alpha _{N\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{O} } = 0.405 \pm 0.021\). The theoretical conversion coefficients were calculated for this transition and for the 391.69 keV M4 transition in113In and were found to be in agreement with the experiment.

Measurements of the total internal conversion coefficient and [formula omitted] probability in the decay of 139Ce

The total conversion coefficient of the 165.853 keV transition in 139La has been determined to be 0·251 ± 0·002 from measurements of the electron and gamma-ray intensities and the source activity. From the X-ray and γ-photon spectra the probability P K ω K has been determined to be 0·639 ± 0·006. Using α T = 0·251 ± 0·002, α K = 0·214 ± 0·002, ω K = 0·906 ± 0·026 and P K ω K = 0·639 ± 0·006 the number of K-X rays and 166 keV photons per disintegration has been calculated to be 0·794 ± 0·009 and 0.799 ± 0·001 respectively, giving a K-X ray to γ-photon ratio of 0·99±0·01. The discrepancy between the experimental and theoretical conversion coefficients is explained by taking the nuclear structure effect into account.

Electromagnetic Transitions in 177Hf

The gamma transitions in 177Hf have been measured using a 50cm radius iron-free double focusing beta-ray spectrometer. The decay scheme is investigated and the K-conversion coefficients of the 208 and 321 keV transitions have been determined. Comparison with theoretical conversion coefficients for pure El radiation calculated by Sliv and Band indicates that the K-conversion process of the 208 keV transition is normal while the large anomaly observed in the K-conversion process of the 32l keV E1 transition is compatible with a large M2 admixture or more probable with the presence of penetration matrix elements. From comparison with theoretical conversion coefficients the 113 keV M1+E2 transition has been found to be (95.12+0.6)% E2 corresponding to |δ| = 4.38±0.33. The decay scheme of 177Lu is discussed in terms of nuclear models.

TheK-conversion coefficient near threshold of the 30 keV isomeric transition in108mAg decay

With calibrated Ge(Li) x-ray detectorsK x rays in the conversion of the 30 keV isomeric transition in the decay of108mAg were observed in coincidence with 79 keV γ-rays. Thus, the fraction of 30 keV transitions which take place byK conversion was measured to be (2.44±0.23) × 10−2. Making use of a theoretical total conversion coefficient (K conversion contributes only a minor part of the total conversion coefficient), an experimental value of theK-conversion coefficient was obtained, αK=(1.07 ± 0.10) × 104 (where the error represents twice the standard deviation to which the error in the detector efficiency has been added linearly). This value agrees with the theory of Hager and Seltzer forM4 conversion. The energy of the cascading γ-ray was remeasured to be 79.20 ± 0.05 keV.

Relative internal conversion electron intensities of the 113 keV transition in177Hf

The intensities of the internal conversion lines of the 113 keVM1 +E2 transition in177Hf have been measured. From comparison with theoretical conversion coefficients the transition has been found to be (95.2 ± 0.5)%E2 corresponding to ¦δ¦=4.5 ± 0.3. The theoreticalLI andMI conversion coefficients used in the comparison have been increased by 5% according to the result that for pureE2 transitions in the deformed region theLI/LII,LI/LIII,MI/MII, andMI/MIII theoretical ratios are too low (∼5%). Moreover, the present result indicates that theLII/LIII andMII/MIII ratios obtained from the tabulations by Hager and Seltzer and from the computer program by Pauli are too high (1–2%).

Gamma-ray transitions in 207Bi following the decay of 207Po

The decay of 5.7 h 207Po to levels in 207Bi has been studied using a Ge(Li) detector. Combining the relative gamma-ray intensities with previously established conversion electron intensities, K-conversion coefficients are determined. The multipolarities of 29 transitions are deduced from a comparison with theoretical conversion coefficients, thus establishing the following spins and parities for the excited levels: 669.5 keV ( 11 2 −), 742.6 keV 7 2 −, 892.3 keV ( 9 2 −), 992.3 keV 7 2 −, 1148.3 keV 5 2 −, (1360.4 keV 7 2 −), 1372.4 keV 5 2 −, 1680.0 keV 3 2 −, (1690.6 keV 5 2 −), 1762.7 keV 5 2 −, 1902.0 keV 1 2 +, 2060.0 keV 3 2 +, and 2405.2 keV 5 2 + . A comparison with a recent shell-model calculation shows good agreement for all negative parity levels.

Comparison of theoretical conversion coefficients

The tables of internal conversion coefficients by Rose and by Sliv and Band were compared and the deviations plotted for all 17 371 cases where the parameters in the two sets of tables match. The mean value of (α R −α SB ) α SB is nearly zero, but the standard deviation is 17%. The deviations (excluding those caused by differences in models) in the K-shell are small (less than 2%) except for two regions where logical explanations exist. The deviations are large and systematic throughout the L-subshells. Many of the deviations are due to defective interpolations as a function of Z. Empirically screened (pure Coulomb) calculations, which include accurate finite size corrections, indicate inaccuracies in the tables by Rose which appear to be associated with finite size effects. These calculations also provide systematic information concerning a cancellation which greatly reduces the magnitude of conversion coefficients in certain regions of the L I subshell for electric transitions. The experimental anomalies recently reported for L-subshell ratios for pure E2 transitions are in such a region and are discussed. There are often large discrepancies between the two sets of tables at low energy. Two regions were found in which large inaccuracies apparently exist in the tables by Sliv and Band. The empirically screened program was found to be a means of accurately interpolating between values calculated with more sophisticated programs.

Zum zerfall des 32 ms isomers 194mIr

The gamma-ray spectrum of the 32 msec isomer in 194Ir, excited by thermal neutron capture, has been reinvestigated with a Ge(Li) spectrometer. Two gamma lines with energies of 111.0 keV ( I γ = 1) and 83.5 keV ( I γ = 0.63) and the x-ray peaks ( I x = 7.7) have been observed. From the intensities and theoretical conversion coefficients for the 111 keV and 83.5 keV gamma rays results a cascade of two M1 transitions or a cascade of transitions with the multipole order (E1 + M2) and M1. Similar experimental results were recently published by Lundan and Siivola but their conclusions are quite different from the interpretation of the isometric decay, given here.

Quadrupole moment of the Kπ = 0 + excited state in odd 172Lu

An investigation of 172 Hf (T 1 2 = 5 y) decay carried out after the sample was chromatographically purified of the daughter 172Lu (6.5 d) isotope. The half-lives of the 110 keV (2 +) and 192 (1 +) states of 172Lu were measured to 2.30±0.12 ns and ≦ 0.5 ns, respectively. The B(E2) of the 44 keV transition is calculated assuming the theoretical conversion coefficient α T = 1.31. The value obtained for B(E2)↑ is (5.60±0.28) × 10 −48 e 2cm 4. Assuming no band mixing, the intrinsic quadrupole moment of the { 7 2 +[404] p ; 7 2 +[633] n }K=0 rotational band was deduced as Q 02 = 7.50±0.20 b. The γ-ray intensities measured with a Ge(Li) detector confirm the decay scheme of Valentin et al. and Harmatz and Handley 1, 2).

Nuclear structure effects in the 343 keV M1 transition in 175Lu

The conversion coefficients of the 343 keV transition in 175Lu were measured via the internal-external conversion method using an automatic 50 cm double-focussing spectrometer and various uranium converters. The experimental values are α K = 0.086±0.004, α L1 = 0.0121±0.0005, α L2 = 0.00115±0.00007 and α L3 = 0.00028±0.00002. From these conversion coefficients and the C S coefficients of Nielsen, the penetration parameter of the 343 keV transition in 175Lu is calculated to be λ 343 = +4.5±1.5. The corresponding mixing ratio is found to be δ 343 2 = 0.069±0.015. These values are consistent with the Rose K, L 1, L 2and L 3 or Sliv and Band K, L 1 and L 3 theoretical conversion coefficients. For complete consistency with all the theoretical conversion coefficients, the Sliv and Band β 1(L 2) would have to be lowered by about 15%. From λ 343, the absolute value of λ for the 482 keV transition in 181Ta is found to be | λ 482|≈ 270±100. Using the sign of λ 343 in Wahlborn's theoretical analysis for the circular polarization P resulting from parity impurities in the 343 keV level of 175Lu, the value of P is expected to be negative and of the order 10 −4.

Internal conversion coefficients of Ni 56

The internal conversion coefficients of the 0.164, 0.272 and 0.484 MeV gamma rays of Ni 56 have been determined utilizing a scintillation gamma ray spectrometer and a Siegbahn-S)ätis intermediate-image beta-ray spectrometer. Respective conversion coefficients of (1.2±0.1) × 10 −2, (3.4±0.2) × 10 −3 and (1.5±0.15) × 10 −3 were found. Comparison with theoretical conversion coefficients expected for pure multipole transitions and use of the Weisskopf single-particle estimates for the gamma-ray transition probabilities lend considerable support to an analysis of the low-excited states of Co 56 in terms of a simple shell model for an odd nucleus.

Half-lives of two excited states in Yb 172

The half-lives of the 1174.0 keV and 78.7 keV excited states in Yb 172 have been measured by the fast time-to-height conversion technique. The half-life of the 1174.0 keV 3 +, K = 3 state is (8.7±0.4)×10 −9 sec, implying hindrances of ≈ 10 3for the two E2, singly K-forbidden transitions to the ground-state rotational band. The half-life of the 78.7 keV 2 + first excited state is (1.5±0.1)×10 −9 sec. An experimental 2 + → 0 + total internal-conversion coefficient is determined from this lifetime measurement and the published B(E2) value, which is larger than the theoretical conversion coefficient by (14±10)%.