Energy dependent angular distribution of individual γ-rays in the ^{139}La(n, γ)^{140}La* reaction
T. Okudaira, S. Endo, H. Fujioka, K. Hirota, K. Ishizaki, A. Kimura, M. Kitaguchi, J. Koga, Y. Niinomi, K. Sakai, T. Shima, H. M. Shimizu, S. Takada, Y. Tani, T. Yamamoto, H. Yoshikawa, T. Yoshioka
aa r X i v : . [ nu c l - e x ] J a n Energy dependent angular distribution of individual γ -rays in the La( n , γ ) La*reaction
T. Okudaira, S. Endo,
1, 2
H. Fujioka, K. Hirota, K. Ishizaki, A. Kimura, M. Kitaguchi, J. Koga, Y. Niinomi, K. Sakai, T. Shima, H. M. Shimizu, S. Takada, Y. Tani, T. Yamamoto, H. Yoshikawa, and T. Yoshioka Nagoya University, Furocho, Chikusa, Nagoya 464-8602, Japan Japan Atomic Energy Agency, 2-1 Shirane, Tokai 319-1195, Japan Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan Kyushu University, 744 Motooka, Nishi, Fukuoka 819-0395, Japan Osaka University, Ibaraki, Osaka 567-0047, Japan (Dated: January 5, 2021)Neutron energy-dependent angular distributions were observed for individual γ -rays from the0.74 eV p-wave resonance of La+ n to several lower excited states of La. The γ -ray signals wereanalyzed in a two dimensional histogram of the γ -ray energy, measured with distributed germaniumdetectors, and neutron energy, determined with the time-of-flight of pulsed neutrons, to identifythe neutron energy dependence of the angular distribution for each individual γ -rays. The angulardistribution was also found for a photopeak accompanied with a faint p-wave resonance componentin the neutron energy spectrum. Our results can be interpreted as interference between s- andp-wave amplitudes which may be used to study discrete symmetries of fundamental interactions. PACS numbers: 13.75.Cs, 21.10.Hw, 21.10.Jx, 21.10.Re, 23.20.En, 24.30.Gd, 24.80.+y, 25.40.Fq, 25.70.Gh,27.60.+j, 29.30.KvKeywords: compound nuclei, partial wave interference, neutron radiative capture reaction
I. INTRODUCTION
In the neutron absorption reaction of
La, extremelylarge parity violation with a size of (9.56 ± − [2–4] is enhanced by the in-terference between s- and p-wave amplitudes, referred toas s-p mixing model [5, 6]. The interference introduces aneutron energy-dependent angular distribution of γ -raysin the vicinity of a p-wave resonance with respect to theincident neutron momentum [7]. The neutron energy de-pendence of the angular distribution for individual γ -rayswas previously measured using a germanium detector as-sembly and the intense neutron beam at the Japan Pro-ton Accelerator Research Complex (J-PARC) [8]. A clearangular distribution depending on the incident neutronenergy was found in the vicinity of the p-wave resonancefor the γ -rays resulting from the transition of the p-waveresonance of La+ n to the ground state of La.In this paper, the angular distributions of the γ -raysresulting from the p-wave resonance to lower excitedstates of La are studied as a function of the incidentneutron energy by applying the same analysis methodas in Ref. [8] to photopeaks for transitions to the lowerexcited states.
II. EXPERIMENTA. Experimental Setup
The data set used in this paper is the same as thatused to evaluate the angular distribution of γ -rays to theground state. The measurement of the angular distribu-tion of the individual γ -rays in the La( n , γ ) La reac-tion was conducted using an intense pulsed neutron beamand a germanium detector assembly at beamline 04 of theMaterials and Life Science Experimental Facility (MLF)at J-PARC [9]. The germanium detector assembly con-sists of 22 high quality germanium crystals, pointing atangles from 36 ◦ to 144 ◦ with respect to the incident neu-tron beam direction [10]. A natural-abundant lanthanummetal plate with dimensions of 1 mm ×
40 mm ×
40 mmwas placed at the detector center. The distance from themoderator surface to the La target is 21.5 m. The protonbeam power was 150 kW and measurement time was 60hours. A more detailed description of the experiment isgiven in Ref. [8].
B. Measurement
The same variables defined in Ref. [8] are used to eval-uate the angular distributions of the γ -rays in this paper.The deposit energy of the γ -rays in the germanium crys-tal E m γ is obtained from the pulse height. The detectiontime of the γ -rays t m is measured from the timing pulseof the injection of the proton beam bunch. These are ob-tained for each γ -ray event. The variable t m correspondsto the Time Of Flight (TOF) of the incident neutronsfor prompt γ -rays, and the corresponding neutron en-ergy E m n is calculated using t m . The neutron energy inthe center-of-mass system E n is defined as well. The to-tal number of γ -ray events detected in the experimentare denoted as I γ . A 2-dimensional histogram corre-sponding to ∂ I γ /∂t m ∂E m γ was obtained for each germa-nium crystal as the experimental result. The histogramof ∂I γ /∂t m , which corresponds to a neutron TOF spec-trum, is shown in Fig. 1. The γ -ray events are integratedfor E m γ ≥ γ -rays. It is normal-ized relative to the incident beam spectrum for t m , whichis obtained from a measurement of the 477.6 keV γ -raysin the neutron absorption reaction of B with an en-riched B target. The small peak at t m ∼ µ s is the [us] lap t [ a r b it r a r y un it ] l a p t ∂ / γ I ∂ L a p - w a v e . e V L a s - w a v e . e V L a s - w a v e . e V L a . e V s - w a v e L a . e V s - w a v e L a . e V p - w a v e FIG. 1. Neutron TOF spectrum defined as ∂I γ /∂t m . It is nor-malized relative to the incident beam intensity as a functionof t m . p-wave resonance, and the 1 /v component is mainly de-rived from the tail of an s-wave resonance in the negativeenergy region as listed in Table I. Figure 2 shows a γ -rayspectrum defined as ∂I γ /∂E m γ . Photopeaks of γ -ray tran-sitions of La( n, γ ) La reactions to the lower excitedand ground states are observed in Fig. 2. A schematic di-agram of the level scheme of the
La( n , γ ) La reactionis also shown in Fig. 3 [15].Here, we focus on the intense transitions to the lowerexcited states of 30 keV, 35 keV, 63 keV, 273 keV,319 keV, 658 keV, 745 keV, 772 keV, and the inclusive γ -ray transitions. Histograms of ∂I γ /∂E m n , which corre- r E r [eV] J r l r Γ γr [meV] g r Γ n r [meV]1 − . (a) (a) . (a) (571 . (a) ∗ . ± . (b) (b) . ± . (b) (5 . ± . × − . ± . (c) (b) . ± . (d) . ± . (d) TABLE I. Resonance parameters of the neutron resonances of
La+ n . The resonance parameters E r , J r , l r , Γ γr , g r ,andΓ nr are resonance energy, total angular momentum, orbitalangular momentum, γ width, g -factor and neutron width, re-spectively. Parameter r denotes the resonance number. (a)taken from Ref. [11] and Ref. [12]. (b) taken from Ref. [8]. (c)taken from Ref. [13]. (d) calculated from Refs. [14] and [13]. ∗ The neutron width for the negative resonance was calculatedusing | E | instead of E . [keV] E × k e V ( g r ound ) k e V ( E x k e V ) k e V , k e V ( E x k e V , k e V ) k e V ( E x k e V ) k e V ( E x k e V ) k e V ( E x k e V ) k e V ( E x k e V ) k e V ( E x k e V ) k e V ( E x k e V ) k e V ( E x k e V ) k e V ( E x k e V ) FIG. 2. Expanded γ -ray spectrum defined as ∂I γ /∂E m γ . Thedotted line shows the literature value of the photopeak en-ergy. Three photopeaks around 4600 keV are single escapepeaks from the γ -rays of 5161 keV, 5131 keV, 5126 keV, and5098 keV. La+n ground 3 -
30 keV 2 -
35 keV 5 - k e V La
63 keV 4 - N e u t r on E n e r gy -48.63 eV s-wave72.30 eV s-wave
163 keV 2 -
273 keV 4 -
319 keV 3 -
602 keV 4 -
658 keV 3 -
712 keV 3 -
745 keV 4 -
772 keV 4 - FIG. 3. Transitions from
La+ n to La. The dashedline shows separation energy of
La+ n . The transitions canactually occur not only from the p-wave resonance, but alsofrom the s-wave resonances. spond to neutron energy spectra, gated with each pho-topeak and inclusive γ -rays are shown in Fig. 4. We cansee that the 0.74 eV p-wave resonance appears in severaltransitions. Note that the spectra are the sum of all de-tector angles. The photopeak region was taken as the fullwidth at the quarter maximum. Since the photopeaks ofthe 5126 keV and 5131 keV completely overlap, they areconsidered to be one photopeak. As a gated energy re-gion for inclusive γ -rays, 2000 keV ≤ E m γ ≤ γ -rays for each photopeak was estimated by a third-orderpolynomial fit in the low and high energy region of eachphotopeak for each detector and subtracted. Since a lossof 2% of the total γ -ray counts occurred due to the DAQsystem, a loss correction was also applied [8]. E γ = 4389 keV E γ = 4416 keV Egate_4502keV E γ = 4502 keV E γ = 4842 keV Egate_4888keVEgate_4888keV E m n (eV) E γ = 4888 keV E m n (eV) E γ = 5098 keV E m n (eV) E γ = 5131, 5126 keV E m n (eV) ≤ E γ ≤ FIG. 4. Neutron spectra gated with each photopeak and inclusive γ -rays. The energy of photopeaks or the gated region of γ -ray energy show at the top left of each histogram. C. Angular Distribution
The neutron-energy dependence of the angular distri-bution causes an asymmetric resonance shape in the neu-tron energy spectrum, which is measured by the asym-metry parameter defined as A LH ( θ d ) = N L ( θ d ) − N H ( θ d ) N L ( θ d ) + N H ( θ d ) , (1)where θ d is the detector angle with respect to the incidentneutron momentum, and N L and N H are integrals in theregion of E − ≤ E n ≤ E and E ≤ E n ≤ E + 2Γ ,respectively. Variables E and Γ denote the resonanceenergy and total width of the p-wave resonance, whichis defined by the γ width and neutron width shown inTable I as Γ = Γ γ + Γ n . The asymmetry is plottedfor effective detector angle ¯ θ d , which is obtained with asimulation of the germanium detector assembly [16], andfitted using a function of the form A LH (¯ θ d ) = A cos ¯ θ d + B with free parameters A and B . The angular distributionsof A LH for the photopeaks and inclusive γ -rays are shownin Fig. 5. The fit results of A , which correspond to theangular distribution of the asymmetry, are listed withthe photopeak energy E γ , excitation energy E ex , andthe angular momentum of the final state F in the Ta-ble II. Non-zero angular distributions were found in thetransition to the excited state of 30 keV and/or 35 keV,63 keV, 658 keV, and 772 keV with a confidence level ofover 99.7% . E γ [keV] E ex [keV] F A , , . ± . − . ± . − . ± . − . ± . . ± . . ± . , , − . ± . − . ± .
024 [8]inclusive - - − . ± . A for each photopeak and inclu-sive γ -rays. III. DISCUSSIONA. Photopeak at 5098 keV
Although the p-wave resonance does not appear in theneutron energy spectrum gated with 5098 keV photo-peak as shown in Fig. 4, the angular distribution A isobserved with a confidence level of over 99.7%. This phe-nomenon can also be confirmed using the neutron energyspectra for 36 ◦ and 144 ◦ detectors shown in Fig. 6. InFig. 6, the s-wave component in the spectra, which obeysthe 1 /v law, is fitted using f ( E m n ) = a/ p E m n + b withfree parameters a and b for the regions except for thep-wave resonance, and the neutron energy spectra beforeand after the subtraction of the s-wave component areshown. We can see that they have a slight asymmet- − − − − Graph A LH − − − − Graph − − Graph − − − − Graph − − − − Graph A LH cos ¯ θ d − − − − cos ¯ θ d − − − − cos ¯ θ d E γ = 4389 keV E γ = 4416 keV E γ = 4502 keV E γ = 4842 keV E γ = 4888 keV E γ = 5098 keV E γ = 5131, 5126 keV − − − − − − − − − − − − Graph cos ¯ θ d ≤ E γ ≤ FIG. 5. Angular distributions of A LH for each photopeak and inclusive γ -rays. The solid lines are the fit results. − − E m n (eV) E m n (eV) FIG. 6. Neutron energy spectra gated with the 5098 keVphotopeak for 36 ◦ (left) and 144 ◦ detectors (right). Solid linesshow fit results to the s-wave component. Black points andwhite points show the spectra before and after subtraction ofthe s-wave component, respectively. ric shape at 0.74 eV, and moreover, the shapes reversewith respect to 0.74 eV for 36 ◦ and 144 ◦ detectors. Thisangular-dependent asymmetric component has also beenobserved for 5161 keV photopeak as shown in Fig. 13in Ref. [8] and is attributed to the interference term be-tween s- and p-wave amplitudes. The significant valueof A observed for faint γ -ray transition from the p-waveresonance can be understood as the result of the moder-ately weak transition amplitude of γ -rays via the p-wavecomponent; the magnitude of A is proportional to theproduct of the transition amplitudes of s- and p-wavecomponents while the γ -ray intensity is proportional tothe square of that of p-wave component. This interpre-tation is clarified by the differential cross section of ( n , γ ) reactions based on the s-p mixing model described in AP-PENDIX E in Ref. [8]. The ordinary p-wave resonanceshown in Fig. 4 corresponds to the second term of a inEq. (E7) in Ref. [8], which has no angular distribution.In contrast, a , which is the interference term between s-and p-wave amplitudes, produces the angular-dependentasymmetric shape at the p-wave resonance for the detec-tor angle satisfying cos θ γ = 0 as shown in Eq. (E1) andEq. (E7) in Ref. [8]. The a term in Eq. (E7) in Ref. [8]is proportional to the branching ratio from the p-waveresonance to the f -th γ -ray transition λ f , whereas thesecond term of a is proportional to λ f . Consequently,the second term of a can be suppressed compared to a when the branching ration from the p-wave resonance tothe particular final state is small. In this way, the phe-nomenon that the 5098 keV photopeak has the angulardistribution while no p-wave resonance appears can beexplained by the interference term a and the suppres-sion of the a amplitude due to the branching ratio. B. Significance of the angular distribution
In order to confirm that the angular distributions areobserved at the p-wave resonance, the angular distribu-tions of A LH were obtained for other neutron energies,not only within the vicinity of the p-wave resonance.The asymmetry A LH is calculated using N L and N H with the integral regions of E c − ≤ E n ≤ E c and E c ≤ E n ≤ E c + 2Γ , respectively, where the center en-ergy of the integral E c takes a value of every 20 meV from0 eV to 2 eV, and then the angular dependence A was ob- − − − − − − − −
10 1 pValue_4389keV − − − − − − − −
10 1 pValue_4416keV − − − − − − − −
10 1 pValue_4502keV − − − − − − − −
10 1 pValue_4842keV − − − − − − − −
10 1 pValue_4888keV − − − − − − − −
10 1 pValue_5097keV − − − − − − − − − − − − − −
10 1 pValue_5126keV − − − − − − − −
10 1 pValue_2000_5170keV E c (eV) E c (eV) E c (eV) E c (eV) E c (eV) E c (eV) E c (eV) E c (eV) ≤ E γ ≤ E γ = 5131, 5126 keV E γ = 4389 keV E γ = 4416 keV E γ = 4502 keV E γ = 4842 keV E γ = 4888 keV E γ = 5098 keV p - v a l u e p - v a l u e p - v a l u e p - v a l u e p - v a l u e p - v a l u e p - v a l u e p - v a l u e FIG. 7. p -values of the angular distribution of A LH as a function of the center energy of the integral. tained for every integral region. In Fig. 7, the significanceof A is measured by a p -value, defined as p = (1 − C . L . ) / p -value indicates the probability toobserve a non-zero value of A in the hypothesis of noangular distributions. A confidence level of over 99.7%corresponds to a p -value less than 1 . × − . As shownin the graph for E γ =4389 keV, 4502 keV, 5098 keV, and5126 keV and/or 5131 keV in Fig. 7, significant angulardistributions are observed only within the vicinity of thep-wave resonance.This analysis suggests that the angular distributionmeasurement in the ( n , γ ) reaction is sensitive to searchfor faint γ -ray transitions from p-wave resonances. IV. CONCLUSION
We observed significant angular distributions depend-ing on the neutron energy for the γ -rays in the transi-tions from the p-wave resonance of La+ n to the sev-eral lower excited states of La, including faint γ -raytransition from the p-wave resonance. This angular dis-tribution can be interpreted as a result of the interference between s- and p-wave amplitudes. Recently, a transverseasymmetry has been measured for the p-wave resonancein the La( n , γ ) La reaction by using polarized epi-thermal neutrons [17], and these measurement results willbe combined in terms of the s-p mixing model in order tounderstand the reaction mechanism of the enhancementof the symmetry violation to be published in a separatepaper.
ACKNOWLEDGMENTS
The authors would like to thank the staff of beam-line04 for the maintenance of the germanium detectors,and MLF and J-PARC for operating the accelerators andthe neutron production target. The neutron scatteringexperiment was approved by the Neutron Scattering Pro-gram Advisory Committee of IMSS and KEK (ProposalNos. 2014S03, 2015S12). The neutron experiment at theMaterials and Life Science Experimental Facility of theJ-PARC was performed under a user program (ProposalNos. 2016B0200, 2016B0202, 2017A0158, 2017A0170,2017A0203). This work was supported by MEXT KAK-ENHI Grant No. JP19GS0210, JSPS KAKENHI GrantNos. JP17H02889, JP19K21047, and 20K14495. [1] V. P. Alfimenkov, S. B. Borzakov, V. V. Thuan, Y. D.Mareev, L. B. Pikelner, A. S. Khrykin, and E. I. Shara-pov, Nucl. Phys. A , 93 (1983).[2] J. M. Potter, J. D. Bowman, C. F. Hwang, J. L. McK-ibben, R. E. Mischke, D. E. Nagle, P. G. Debrunner,H. Frauenfelder, and L. B. Sorensen, Phys. Rev. Lett. , 1307 (1974).[3] V. Yuan, H. Frauenfelder, R. W. Harper, J. D. Bowman,R. Carlini, D. W. MacArthur, R. E. Mischke, D. E. Nagle,R. L. Talaga, and A. B. McDonald, Phys. Rev. Lett. ,1680 (1986).[4] E. G. Adelberger and W. C. Haxton, Ann. Rev. Nucl.Part. Sci. , 501 (1985).[5] O. P. Sushkov and V. V. Flambaum, Usp. Fiz. Nauk ,3 (1982).[6] O. P. Sushkov and V. V. Flambaum, Sov. Phys. Uspekhi , 1 (1982).[7] V. V. Flambaum and O. P. Sushkov, Nucl. Phys. A ,352 (1985).[8] T. Okudaira, S. Takada, K. Hirota, A. Kimura,M. Kitaguchi, J. Koga, K. Nagamoto, T. Nakao,A. Okada, K. Sakai, H. M. Shimizu, T. Yamamoto, andT. Yoshioka, Phys. Rev. C , 034622 (2018).[9] M. Igashira, Y. Kiyanagi, and M. Oshima, Nucl. In-strum. Meth. Phys. Res. A600 , 332 (2009). [10] A. Kimura, T. Fujii, S. Fukutani, K. Furutaka, S. Goko,K. Y. Hara, H. Harada, K. Hirose, J. Hori, M. Igashira,T. Kamiyama, T. Katabuchi, T. Kin, K. Kino, F. Ki-tatani, Y. Kiyanagi, M. Koizumi, M. Mizumoto, S. Naka-mura, M. Ohta, M. Oshima, K. Takamiya, and Y. Toh,J. Nucl. Sci. Tech. , 708 (2012).[11] S. F. Mughabghab, Atlas of Neutron Resonances 5th ed. (Elsevier, Amsterdam, 2006).[12] K. Shibata, O. Iwamoto, T. Nakagawa, N. Iwamoto,A. Ichihara, S. Kunieda, S. Chiba, K. Furutaka,N. Otuka, T. Ohsawa, T. Murata, H. Matsunobu, A. Zuk-eran, S. Kamada, and J. Katakura, J. Nucl. Sci. Technol , 1 (2011).[13] R. Terlizzi and others (n TOF Collaboration), Phys. Rev.C , 035807 (2007).[14] G. Hacken, J. Rainwater, H. I. Liou, and U. N. Singh,Phys. Rev. C , 1884 (1976).[15] N. Nica, Nuclear Data Sheets , 1287 (2007).[16] S. Takada, T. Okudaira, F. Goto, K. Hirota, A. Kimura,M. Kitaguchi, J. Koga, T. Nakao, K. Sakai, H. M.Shimizu, T. Yamamoto, and T. Yoshioka, Journal ofInstrumentation , P02018 (2018).[17] T. Yamamoto, T. Okudaira, S. Endo, H. Fujioka, K. Hi-rota, T. Ino, K. Ishizaki, A. Kimura, M. Kitaguchi,J. Koga, S. Makise, Y. Niinomi, T. Oku, K. Sakai,T. Shima, H. M. Shimizu, S. Takada, Y. Tani,H. Yoshikawa, and T. Yoshioka, Phys. Rev. C101