Physics - 119 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 The Study of Electric Quadrupole Transition (E2) in 56Ba and 62Sm Nuclei F.A. Jassim ,Z. A. Dakhil* ,Y.H. Jaber Department of Physics , College of Education, IbnAl-Haitham, University of Baghdad * Department of Physics , College of Science , University of Baghdad Received in: 9 May 2011, Accepted in: 16 November 2011 Abstract Transition strengths ↓ 2 .u.w2)M(E for gamma transition from first excited 21 +states to the ground states that produced by pure electric quadrupole emission in even –even isotopes of 56Ba and 62Sm have been studied through half- lives time for 21+ excited states with the intensities of γ0- transitions measurements and calculated as a function of neutron number (N). The results thus obtained have shown that; the nuclides with magic neutron number such as 56Ba138 and 62Sm144 have minimum value for ↓ 2 .u.w2)M(E . Key Words: electric quadruple transitions strength [M(E2)]2. Introduction The WeissKoph single-particle transition probability B(EL,ML) is defined by [1] as the ratio of the single-particle half-life time to the experimental half-life time for gamma transition B(EL,ML)W.u ↓= ( ) ( )exp 2 1 2 1 , , MLELt MLELt SP γ γ ……………….(1) Where L is the multipolarities L=1,2,3,……… L≠ 0 While the γ-ray transition strength [M(EL,ML)]2 is defined as the ratio of gamma width to gamma width in Weiss Kopf unit (W.u ) [2] [M(EL,ML)]2 W.u↓ = ( ) ( ) uWMLEL MLEL . exp , , Γ Γ ………….(2) Since Гγ Т≈ћ …………(3) Where; Гγ is the total width Гγ =∑ Гγl …………(4) Гγl is the partial gamma width Т is the mean life time of initial level Т = 2ln 2 1τ …………..(5) Ћ = π2 h = 0.65822x 10-15 eV.s h is Plank constant. From eqs. (2, 3 and 4) . can be concluded B(EL,ML)W.u ↓= [M(EL,ML)]2 W.u ……………(6) Physics - 120 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 Specific expression for B(EL,ML)W.u suggested by M.J.Martin [2] is : B(EL,ML)W.u ↓ = ………….(7) If the transition is of mixed multi polarity M1 and E2 ref.[3] then δ= ± …….(8) Where δ is the mixing ratio and Гγ=Г(M1) +Г(E2) ……..(9) For a pure E2 transition , δ=0 and hence Г(E2) = Гγ …………….(10) Then the transition strength for electric quadruple transition E2 can be calculated by using eq .(2) in the form : [M(E2]2 W.u↓ = ………….(11) Or eq .(7) in the form : [M(E2]2 W.u↓= …………..(12) On the basis of an extreme single particle model the value for the Г(E2)W.u in eV. ref.[4] Г(E2)W.u = 4.7907X 10-23 53 4 γEA …(13) Where E γ in keV. for nuclear of mass No. A and the corresponding reduced transition probability is : B W.u.(E2) = 0.05940 e2 (fm)4 ……(14) The relation between B(E2) ↓ =B(E2 ;2→1) and B(E2) ↑=B(E2;1→2) as given by ref [2] is: B(E2) ↑= B(E2) ↓………(15) Results of Calculations The electric quadrupole transition strengths ↓ 2 .u.w2)M(E for γ –ray from +→+ 11 02 have been calculated as a function of neutron number (N) using eq. (11) with aid of the experimental data reported in ref. [1] to even –even isotopes for; 56Ba (122≤A≤146) and 58Ce (124≤A≤148) which have only one transition for γ is γ0 with intensity (100%)E2. The results of calculations are presented in table (1) for 56Ba nuclides and in table (2) for 62Sm nuclides. . The transition strengths ↓ 2 .u.w2)M(E are plotted as a function of neutron number (N) as shown in Fig. (1) and Fig. (2) for56Ba and 62Sm respectively . For the sake of comparison, the ↓ 2 .u.w2)M(E values are converted to B (E2) e 2 b2↑ using eq. (12) and then eq.(15), the present B (E2) e2 b2↑values of γ0 -transitions in 56Ba and 62Sm nuclides are compared with the experimental values as well as with other of various theoretical models. this comparison are presented in tables (3and4) and shown in Figs. (3 and4) respectively. Discussion In view of tables (1and2) one can point out that the experimental values of partial gamma width Γ (E2) are larger than that estimated by Weisskopf unit )2E(.u.wΓ especially when the nucleon number deviated more and more from the magic neutron number. Since the cooperative effects appear between nucleons. Also, it appears that the single particle shell Physics - 121 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 model is valid particularly near the closed shell, a minimum value for Γ (E2) to )2E(.u.wΓ is obtained at magic neutron number so that the calculated ↓ 2 .u.w2)M(E which are limited to the even – even nuclides and shown in Fig.(1) and Fig.( 2) reproduce the diffraction minimum at the magic neutron number N= 82 which is included in 56Ba and 62Sm nuclei. The discrepancy of the calculated ↓ 2 .u.w2)M(E for196.1 keV +→+ 11 02 transition from 196.1 keV level in Ba12256 gives an indication that the half life time for +12 state reported in ref. [1] is inaccurate and that the value of ↓ 2 .u.w2)M(E may be ruled out. If the experimental value of B (E2)e2 b2 ↑ for 196.1 KeV. ( +→+ 11 02 ) transition from 196.1KeV. level ref.[5] is used to calculate the half- life time for this level (348.0 ±34.5)Ps. will be obtained instead of the value reported in table (1). The reduced transition probabilities B(E2) values of γ0 -transitions for the following nuclides ; Sm14062 , Sm 142 62 , and Sm 146 62 listed in table (2) are not presented because the experimental data such as ( half life time t½ for 2+ excited states and the intensities of γ0- transitions) are not available. The observed location of the diffraction minimum at N=82 are very well reproduced in 56Ba and 62Sm nuclei. Figures(3,4) show the comparison of the present values of B(E2) with those reported in ref.(5) of ; experimental, Global best fit, Single Shell Asymptotic Nilsson Model (SSANM ) and Finite –Range Droplet Model( FRDM) values. The present results together with the other results seem to be a good behavior at all regions of N and close to each other except the SSANM results of ref. [5] are departed by some amount but slightly for Ba nuclides, while the results of FRDM of ref .[5] are deviated for Sm at 80 < N< 84. The observed diffraction minimum is very well reproduced by all models except for FRDM results [5]. Finally the present values together with the Global best fit values are in a good agreement with those of the experimental results so it should be helped in testing the measured electric quadrupole transitions E2 values predicted by different theoretical models. References 1. Fore stone, R.B. and Shirley, V.S. (1999), Table of Isotopes , 8th edition, John Wiley and Sons. 2. Martin, M.J. (September 27,1982), Reduced Gamma-Ray Matrix Elements, Transition Probabilities, and Single-Particle Estimates., Oak Ridge National Laboratory, Operated by Union Corporation, Nuclear Division . 3. Yazar ,H.R.,Uluer I.,Unaloglu V.,and Yasar S.,(2010),The Investigation of Electromagnetic Transition Probabilities of Gadolinium Isotopes with the IBFM- Model ,Chinese Journal of Physics ,48(3):344. 4. Brussard, P.J. and Gland emans, P.W.M .,( 1977) ,((Shell –Model Applications in Nuclear Spectroscopy)) North- Holland .Publishing Company Amsterdam , New York, oxford . 5. Raman, S.; Nestor, C.W. and Tikkanen, J.R. (2001) ,Atomic Data and Nuclear Data. Tables, 78 : (1) . Physics - 122 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 Table (1): Transition strengths [M(E2)]2 W.u.↓ of γ0 - rays from the +→+ 11 02 in 56Ba nuclides with the partial gamma widths in W.u., total gamma widths ,mean life times for first excited states, with experimental values reported in ref.[1]and used in present work Experimental values Ref. [1] Τ (Ps) Г tot× 10-6 ( eV) Г W.u.( E2) × 10-6(eV) [M(E2)] 2 W.u.↓ A N Ei(keV) Eγ0 (keV) t½ (Ps) 122 66 196.1 196.1 0.297 (27) 0.42857(39) 1535.828(139620) 0.0084 (18.270±1.6)x104 124 68 229.89 229.9 297 (26) 428.571(37518) 1.5358(1344) 0.01902 80.745±7.069 126 70 256.09 256.1 108 (4) 155.844(5772) 4.2235(1564) 0.0333 126.71±4.69 128 72 284 284 100.0(45) 144.3000(64935) 4.5614(2052) 0.05709 79.89±3.60 130 74 357.38 357.41 37(4) 53.3911(57720) 12.3281(13327) 0.18392 67.028±7.246 132 76 464.588 464.55 15.1 (11) 21.7893(15873) 30.2080(22005) 0.6969 43.346±3.158 134 78 604.723 604.72 5.12 (9) 7.38817(12990) 89.0900(15660) 2.6565 33.636±0.589 136 80 818.515 818.514 1.930(15) 2.78499(2160) 236.3424(18368) 12.3097 19.20±0.15 138 82 1435.818 1435.795 0.195 (5) 0.28139(720) 2339.184(59979) 204.972 11.220±0.288 140 84 602.35 602.35 9.7(41) 13.9971(59163) 47.0248(198764) 2.7615 17.029±7.198 142 86 354.597 354.598 66 (4) 95.2381(57720) 6.9112(4188) 0.21338 32.389±1.963 144 88 199.32 199.326 700 (30) 1010.10(4329) 0.6516(279) 0.01137 57.275±2.455 146 90 181.05 181.02 860(30) 1240.98(4329) 0.5303(165) 0.00715 74.030±2.582 Table (2): Transition strengths [M(E2)]2 W.u.↓ of γ0 - rays from the +→+ 11 02 in 62Sm nuclides with the partial gamma widths in W.u., total gamma widths ,mean life times for first excited states, with experimental values reported in ref.[1]and used in present work Exp erimental vales Ref.[1] Τ (Ps) tot Γ × 10-6 (eV.) Г W.u.( E2) × 10-6 ( eV.) [M(E2)]2 W.u.↓ A N Ei(keV) Eγ0 (keV) t½ (Ps) 134 72 163 163 420 (40) 606.06(5772) 1.0860(1034) 0.00378 287.3247 ± 27.3643 136 74 254.91 254.9 88 (9) 126.980(987) 5.18340(53011) 0.036062 143.7366 14.7002 138 76 346.9 346.9 33(7) 47.619(10101) 13.8224(29320) 0.17163 80.5365 ±17.0835 144 82 1660.2 1659.8 0.084(3) 0.1216(36) 5410.924(16046) 454.740 11.8646 ± 0.3519 148 86 550.265 550.284 7.7 0 (15) 11.1110(2165) 59.239(1154) 1.89199 31.3103 ± 0.6099 150 88 333.863 333.97 48.4 (11) 69.8410(15873) 9.4240(2141) 0.1583 59.5351 ± 1.3531 Table (3):The calculated reduced transition probabilities B (E2) e2b2 ↑ values are compared with that of experimental, Global best fit and, theoretical predications for 56Ba nuclides. A N 0γ E(keV) B(E2; +→+ 11 02 ) e2 b2 Experimental values of Ref[5] Present work values Theoretical values Ref.[5] Global Best fit of SSANM FRDM 118 62 194 - - 1.72±0.30 1.882 2.448 120 64 183 - - 1.82 ± 0.32 1.881 2.254 122 66 196 2.81 ± 0.28 (3289.63±299.05) 1.67 ± 0.29 1.854 2.06 124 68 229 2.09 ± 0.10 1.486± 0.130 1.41 ± 0.25 1.821 2.031 126 70 256 1.75±0.09 2.382±0.088 1.25 ±0. 22 1.787 1.753 128 72 284 1.48 0.07 1.533± 0.690 1.11 ± 0.19 1.595 1.287 130 74 357 1.163±0.016 1.313± 0.142 0.88 ± 0.15 1.336 0.797 132 76 464 0.86 ±0.06 0.867 ± 0.063 0.67 ±0.12 1.092 0.555 134 78 604 0.658±0.007 0.684± 0.012 0.51 ±0.09 0.874 0.281 136 80 818 0.410±0.008 0.400± 0.065 0.37 ± 0.06 0.682 < 0.001 138 82 1435 0.230±0.009 0.238 ± 0.006 0.210±0.037 0.468 < 0.001 140 84 602 0.45±0.19 0.368± 0.156 0.50 ± 0.09 0.907 < 0.001 142 86 359 0.699±0.037 0.714 ± 0.021 0.82 ± 0.14 1.256 0.631 144 88 199 1.05 ±0.0 6 1.286± 0.055 1.47 ± 0.26 1.634 0.989 146 90 181 1.355±0.048 1.694± 0.059 1.60 ±0.28 1.886 1.584 148 92 141 - - 2.03 ± 0.35 2.115 2.467 Physics - 123 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 Table (4): The calculated reduced transition probabilities B (E2)e2 b2 ↑values are compared A N 0γ E(keV) B(E2 ; +→+ 11 02 ) e2 b2 Experimental values of Ref[5] Present work values Theoretical values Ref .[5] Global Best fit of SSANM FRDM 130 68 122 - - 3.1 ± 0.6 3.143 4.107 132 70 131 - - 2.9 ± 0.5 3.096 3.889 134 72 163 4.2 ± 0.6 5.863± 0.558 2.31 ± 0.40 2.824 3.714 136 74 254 2.73 ± 0.27 2.991± 0.306 1.46 ± 0.26 2.451 2.027 138 76 346 1.41 ± 0.23 1.710± 0.363 1.06 ± 0.19 2.093 1.253 140 78 530 - - 0.69 ± 0.12 1.764 0.606 142 80 768 - - 0.47 ± 0.08 1.467 < 0.001 144 82 1660 0.262 ± 0.006 0.266 ± 0.008 0.216 ± 0.038 1.122 < 0.001 146 84 747 - - 0.48 ± 0.08 1.815 < 0.001 148 86 550 0.720 ± 0.030 0.729 ± 0.014 0.64 ± 0.11 2.337 1.161 150 88 333 1.350 ± 0.030 1.412± 0.032 1.05 ± 0.18 2.886 2.019 152 90 121 3.46 ± 0.06 - 2.8 ± 0.5 3.246 3.059 Fig. (1): The transition strengths ↓ 2 .u.w2)M(E for γ0-transition as a function of neutron number (N) in 56Ba nuclides. Physics - 124 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 Fig. (2): The transition strengths ↓ 2 .u.w2)M(E for γ0 -transition as a function of neutron number (N) in 62Sm nuclides. Fig.(3): Comparison between the B (E2) ↑ values of the present work for 56Ba nuclides with Global , experimental and other theoretical results Physics - 125 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 Fig. (4): Comparison between the B (E2) ↑ values of the present work for62Sm nuclides with Global , experimental and other theoretical results. Physics - 126 مجلة إبن الهيثم للعلوم الصرفة و التطبيقية 2012 السنة 25 المجلد 3 العدد Ibn Al-Haitham Journal for Pure and Applied Science No. 3 Vol. 25 Year 2012 (E2)في نويدات 56Ba, 62Sm اعي القطب الكهربائيدراسة النتقاالت رب فاطمة عبد األمير جاسم ، زاهدة أحمد دخيل* ، يوسف هاشم جابر أبن الهيثم، جامعة بغداد -قسم الفيزياء ،كلية التربية جامعة بغداد ،* قسم الفيزياء، كلية العلوم 2011ين الثاني تشر 16 :قبل البحث في 2011ايار 9استلم البحث في : الخالصة ↓حسبت قوى االنتقال 2 .u.w2)M(E النتقاالت أشعة كاما من المستوي المتهيج األول + المستوي إلى 12 كدالة إلى 62Sm, , 56Baلكل من زوجية -األرضي والناتج من إشعاع رباعي قطب كهربائي نقي في النويدات الزوجية ↓العدد النيوتروني اذ حسبت قوى االنتقال 2 .u.w2)M(E باالعتماد على معدل عمر المستوي المتهيج األول + 12 سبية ألشعة كاما المنبعثة من ذلك المستوي المحفز إلى المستوي األرضي وقد لوحظ أن اصغر قيمة لـ والشدة الن ↓ 2 .u.w2)M(E ) 56تكون في النويدات اآلتيةBa 138 , 62Sm144ولغرض 82) التي لها العدد النيوتروني السحري . ↓المقارنة فقد حولت قيم قوى االنتقال 2 .u.w2)M(E الى احتمالية االنتقال المختزلة↑ 22)2( beEB لتلك أن عملنا الحالي يعطي مجموعة كاملة الحتمالية االنتقال المختزلة في النويدات المذكورة لغرض المقارنة مع .االنتقاالت نتائج تم حسابها عمليا . ↓ 2 .u.w2)M(E نتقال لرباعي القطب الكهربائي : قوى اال ةمفتاحيالكلمات ال