Example_Thesis - Implication of empirical formula for yrast...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Implication of empirical formula for yrast excitation energies of even-even nuclei by Dooyoung Kim INHA Graduate School Thesis submitted to the Inha University for the degree of Doctor of Physics Supervisor: Prof. Jin-Hee Yoon Department of Physics c July 2010 . I hereby declare that this thesis is the result of my own work, includes nothing which is the outcome of work done in collaboration except where specifically indicated in the text and bibliography, is not substantially the same as any other work that I have submitted or will be submitting for a degree or diploma or other qualification at this or any other university, and does not exceed the prescribed word limit of 60,000 words. Joe Bloggs 7th July 2010 i Here you include the summary of your thesis: a snappy one page (or a little bit more) description of what your thesis does. You will describe the contents of your thesis in much more detail in the introduction. ii Here you thank all the people that have helped you along the way. I suggest you thank the people who have actually helped you, not just all the really senior impressive sounding people who may (or may not) have used some of your work to wipe up a coffee spillage at some point. iii i ii iii 1 2 3 1 2 4 1 5 Yrast Yrast ....................... 1 3 9 9 . . . . . . . . . . . . . . . . . . . . . . 11 17 . . . . . . . . . . . . . . . . . . 17 21 iv 1 , . . , , . , Weizs¨cker a , . Raman Z 0+ , j 8 20, 20 28, 28 50, 50 82, 82 126, j 11 7 21 31 43 , , , 2, 2 222 57 2 , , - Bohr , , , , (Semi empirical mass formula) . 280 2+ , B (E 2) . 126 184 , 1 12, 8, 22, 32, 44 j proton) Np jz 58 .[2] (valence . 1965 , Np Nn Np Nn , (valence neutron) Nn Hamamoto B (E 2) .[3] .[4],[5]. Ha Np Nn - . (natural parity even multipole states) Ex .[6],[7] , A Ex = αA−γ + βp e− λp Np + βn e− λn Nn , Np , Nn , . Ha . 2 .3 . 4 γ0 J c ,λp = λ0 √p ,λn J α,γ ,βp ,βn ,λp ,λn α = α 0 J a ,γ = = λ0 √n J . , . 2 2 Yrast . . multipole state) NPEMS , , (natural parity even (natural parity (unnatural par(un. J + (J = 2, 4, 6, 8, 10) , J+ + J1 + , J1 + Ex (J1 ) , yrast odd multipole state) NPOMS ity even multipole state) UPEMS , UPOMS natural parity odd multipole state) J − (J = 1, 3, 5, 7, 9) , J − − J1 − , J1 − Ex (J1 ) . J J − (J = 2, 4, 6, 8, 10) , J − − J1 − , J1 − Ex (J1 ) , + J1 J + (J = 1, 3, 5, 7, 9) , J + + , J1 + Ex (J1 ) . Kibedi[9] , Ex (2+ ) 1 Raman[8] , Ex (3− ) 1 Firestone Table of Isotopes, 8th edition[10] 3 Yrast . Ha states) (valence proton) .[6] (natural parity even multipole (first excited energy) (valence neutron) 4 Ex = αA−γ + βp e−λNp + βn e−λNn 2.1 2+ 10+ 1 1 Ex = αA−γ + βp e−λp Np + βn e−λn Nn A , Np Ex χ2 = N0 10 RE (i) N0 i=1 RE (i) . N (2.1) . 2+ 1 .[8] (2.2) , α,γ ,βp ,βn ,λp ,λn χ2 . (2.3) , Nn exp cal RE (i) = log [Ex (i)] − log [Ex (i)] (2.4) exp Ex (i) cal Ex (i) i . Ex log i . 4 Yrast 1965 . Np = min(Z − Nc−1 , Nc − Z ) Nn = min(N − Nc−1 , Nc − N ) Nc − 1 Nc − 1 . 0+ Hamamoto B (E 2) Np Nn Np Nn 1.1 . Ha 1.1 χ2 . 1.1 χ2 0.126 . . 1.1 2+ 1 A Ha . . 557 . 2+ 1 . Nc Nc 2+ (2.5) Hamamoto 12.6% . 2+ 1 Kim 2+ , 4+ , 6+ , 8+ , 10+ 1 1 1 1 1 [7]. 1.2 . α . 5 Yrast + J1 2+ 1 2.1: α MeV 68.37 2+ 1 γ 1.34 βp MeV 0.83 βn MeV 1.17 γp 0.42 γn 0.28 χ2 0.126 N0 557 2.1: 2+ 1 , γ , βp , βn . , 2.2 2+ 1 χ2 2+ , 4+ , 6+ , 8+ , 10+ 1 1 1 1 1 2+ 1 , λp , λn , . . 2+ , 4+ , 6+ , 8+ , 10+ 1 1 1 1 1 2+ , 4+ , 6+ , 1 1 1 8+ , 10+ 1 1 6 Yrast 2.2: + J1 2+ , 4+ , 6+ , 8+ , 10+ 1 1 1 1 1 α MeV 68.37 268.04 598.17 1438.59 2316.85 . 2.2 . A=144 166 A=218 232 γ 1.34 1.38 1.38 1.45 1.47 βp MeV 0.83 1.21 1.40 1.34 1.36 βn MeV 1.17 1.68 1.64 1.50 1.65 γp 0.42 0.33 0.31 0.26 0.21 γn 0.28 0.23 0.18 0.15 0.14 χ2 0.126 0.071 0.069 0.053 0.034 N0 557 430 375 309 265 2+ 1 4+ 1 6+ 1 8+ 1 10+ 1 . . . 7 Yrast 2.2: 2+ , 4+ , 6+ , 8+ , 10+ 1 1 1 1 1 2+ , 4+ , 6+ , 8+ , 10+ 1 1 1 1 1 8 3 Yrast 1 NPEMS . 3.2 NPEMS NPOMS . 3.1 . 6+ , 8+ , 10+ 1 1 1 3.1 NPEMS . A=218 232 . . (Fermi level) 2f7/2 2d3/2 2f 57/2 , (dipole) 2g9/2 2g7/2 N Z ,N 60 . Z N=136 88 2d5/2 A=144 166 Ex 2+ , 4+ , 1 1 . NPOMS 3.1 . 9 Yrast 3.1: + J1 1− , 3− , 5− , 7− , 9− 1 1 1 1 1 α MeV 75.31 76.50 144.14 282.54 441.51 3.2 γ 0.83 0.83 0.92 1.01 1.06 βp MeV 2.18 1.07 0.84 0.66 0.77 βn MeV 2.33 0.90 1.09 1.08 1.33 . . 1− , 3− , 5− , 7− , 9− 1 1 1 1 1 . NPOMS NPOMS . A=220 232 . (Fermi level) 2g9/2 , 1j15/2 N (octopole) (long-range) [10]. Z ,N 60 [8][9]. Z N=134 88 2d5/2 1.2 A=144 152 Ex γp 0.57 0.40 0.32 0.37 0.32 γn 0.44 0.47 0.45 0.56 0.37 χ2 0.240 0.073 0.046 0.036 0.022 N0 177 289 297 241 204 1− 1 3− 1 5− 1 7− 1 9− 1 NPOMS 2g7/2 1h11/2 1i13/2 NPOMS α α 6 βp 35 6 α, γ , βp , βn , λp , λn . NPEMS NPOMS .γ 9− 1 7− 1 9− 1 α 10+ 1 α NPEMS α 1− 1 α . 2+ 1 10 Yrast . βn βp . λp . λn 9− 1 7− 1 2 NPEMS . . Ha Ex = αA−γ + βp e−λp Np + βn e−λn Nn 6 NPEMS UPEMS EMS UPOMS 10− 1 2− 1 5 10− 1 . βp 8− 1 γ . βn . λp λn . 3.3 UPEMS 10− 1 8− 1 NPOMS .α γ UP(3.1) α, γ , βp , βn , λp , λn NPOMS UPEMS UPOMS . α 3.5 UPOMS 9+ 1 1+ 1 .α α . UPOMS 11 Yrast 3.2: + J1 1− , 4− , 6− , 8− , 10− 2 1 1 1 1 α MeV 48.27 75.04 107.98 277.43 238.48 γ 0.73 0.81 0.83 1.00 0.90 βp MeV 1.09 1.00 0.77 0.90 1.24 βn MeV 1.59 1.27 1.40 1.50 1.76 γp 0.19 0.17 0.19 0.15 0.44 γn 0.31 0.24 0.28 0.20 0.25 χ2 0.058 0.027 0.019 0.017 0.012 N0 246 253 248 230 199 2− 1 4− 1 6− 1 8− 1 10− 1 3.3: + J1 1+ , 3+ , 5+ , 7+ , 9+ 1 1 1 1 1 α MeV 47.13 49.45 87.00 139.02 172.81 γ 0.67 0.76 0.83 0.88 0.86 βp MeV 0.54 1.17 1.05 1.19 1.09 βn MeV 0.99 1.49 1.25 1.48 1.61 γp 0.76 0.58 0.40 0.28 0.34 , γn 0.50 0.32 0.24 0.24 0.46 α χ2 0.079 0.051 0.028 0.021 0.019 N0 251 236 250 184 159 1+ 1 3+ 1 5+ 1 7+ 1 9+ 1 . 12 Yrast 3.1: 2+ , 4+ , 6+ , 8+ , 10+ 1 1 1 1 1 2+ , 4+ , 6+ , 8+ , 10+ 1 1 1 1 1 13 Yrast 3.2: 1− , 3− , 5− , 7− , 9− 1 1 1 1 1 1− , 3− , 5− , 7− , 9− 1 1 1 1 1 14 Yrast 3.3: 2− , 4− , 6− , 8− , 10− 1 1 1 1 1 2− , 4− , 6− , 8− , 10− 1 1 1 1 1 15 Yrast 3.4: 1+ , 3+ , 5+ , 7+ , 9+ 1 1 1 1 1 1+ , 3+ , 5+ , 7+ , 9+ 1 1 1 1 1 16 4 1 3 . NPEMS Ex NPEMS, NPOMS, UPEMS, NPOMS . Ex UPEMS UPOMS UPOMS . Ex Ex NPEMS NPOMS , UPEMS UPOMS . UPEMS UPOMS 3.2 3.3 α λp βn γ λn 4 Ex α , γ , βp , βn , λp , λn , βp . α , γ , λp βn 6 λn . βp 17 . α = α0 J a and γ = γ0 J c λp = λ0 √p J and λn = λ0 √n J (4.1) J . . Ha α0 , a, γ0 , c, λ0 p λ0 n Ex = α0 J A UPEMS 2.4 a −γ0 J c + βp e − √p Np J λ0 + βn e − √n Nn λ0 J (4.2) UPOMS 4.2 χ2 NPEMS . , UPEMS UPOMS 30 8 4.1 4.2 N0 8 . UPEMS χ2 (sum) χ2 (sum) = = 1 Ntot 1 Ntot . . χ2 UPOMS . 2 iJ |RE (iJ )| 2 iJ |RE (iJ )| 2 1 J NJ NJ 1 J NJ = iJ , Ntot J i J NJ χ (J ) NJ , χ2 (J ) J J χ2 (4.3) . 18 4.1: 2− , 4− , 6− , 8− , 10− 1 1 1 1 1 2− , 4− , 6− , 8− , 10− 1 1 1 1 1 2− , 4− , 6− , 8− , 10− 1 1 1 1 1 19 4.2: 1− , 3− , 5− , 7− , 9− 1 1 1 1 1 1− , 3− , 5− , 7− , 9− 1 1 1 1 1 1− , 3− , 5− , 7− , 9− 1 1 1 1 1 20 5 Conclusion to the thesis. Wovon man nicht sprechen kann, dar¨ber muss u man schweigen. 21 [1] H. J. Williams, Rev. Sci. Instrum. 8, 56 (1937). [2] S. Chikazumi, J. Phys. Soc. Jpn. 11, 718 (1956). [3] C. A. Neugebauer, Phys. Rev. 116, 1441 (1959). [4] H. Miyajima, K. Sato and T. Mizoguchi, J. Appl. Phys. 47, 4469 (1976). [5] T. Wielinga, J. Appl. Phys. 50, 4888 (1979). [6] G. Pastor and M. Torres, J. Appl. Phys. 58, 920 (1985). [7] S.-C. Shin and C.-S. Kim, IEEE Trans. on Magn. 27, 4852 (1991). [8] M. Noda, IEEE Trans. on Magn. 27, 4864 (1991). [9] J. O. Artman, IEEE Trans. Magn. MAG-21 1271, (1985). [10] P. Poulopoulos, N. K. Flevaris, R. Krishnan and M. Porte, J. Appl. Phys. 75, 4109 (1994). [11] M. Prutton, Thin Ferromagnetic Films (Pub. Inc. London, 1964). [12] P. J. H. Bloemen, E. A. M. Van Aplphen, W. J. M. De Jonge and F. J. A. Den Brorder, Mat. Res. Soc. Symp. Proc. 231, 479 (1992). 22 [13] K. A. Hempel and C. Vogit, Z. angew. Phys. 19, 108 (1965). [14] H. J. Richter, J. Appl. Phys. 67, 3081 (1990). [15] J. Kohlepp and U. Gradmann, J. Magn. Magn. Mat. 139, 347 (1995). [16] P. M. Sollis and P. R. Bissell, J. Phys. D: Appl. Phys. 24, 1891 (1994); referrence there in. [17] G. Asti and S. Rinaldi, J. Appl. Phys. 45, 3600 (1974). [18] C. Vittoria, Microwave Properties of Magnetic Films (World Scientific Singapore, 1993), Chap. 5. [19] Z. Celinski, K. B. Urquhart and B. Heinrich, J. Magn. Magn. Mat. 166, 129 (1997); and refference there in. [20] R. A. Hajjar, F. L. Zhou and M. Mansuripur, J. Appl. Phys. 67, 5328 (1990). [21] G. H. Lander, M. S. S. Brooks, B. Lebech, O. Vogt and K. Mattenberger, Appl. Phys. Lett. 57, 989 (1990). [22] E. C. Stoner and E. P. Wohlfarth, Philos. Trans. R. Soc. London Sect. A240, 599 (1948). [23] [24] , , , , , 10, 463 (1997). , 8, 34 (1998). [25] R. A. Mccurrie and S. Jackson, IEEE Trnas. on Magn. 16, 1310 (1980). [26] J. Smit, F. K. Lotgering and U. Enz, J. Appl. Phys. 31, 137S (1960). 23 [27] P. J. Flanders and S. Shirikman, J. Appl. Phys. 33, 216 (1962). [28] W. H. Press, AS. A. Teukolsky, W. T. Verrerling and B. P. Flannery, Numerical Recipes in C (Cambridge Univ. Press, 2ed Ed. New York, 1992), Chap. 15. [29] , , 2, 263 (1992). [30] J. Hur and S.-C. Shin, Appl. Phys. Lett. 62, 2140 (1993). 24 ...
View Full Document

This note was uploaded on 03/22/2011 for the course PHYSICS 90211 taught by Professor Scopel during the Spring '09 term at Seoul National.

Ask a homework question - tutors are online