Experimental Studies of the Neutron Deficient Atomic Nuclei 94Ru, 95Rh and 172Pt via their Electromagnetic Properties: Du som saknar dator/datorvana kan kontakta Pär Olsson, polsson@kth.se för information

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Experimental Studies of the Neutron Deficient Atomic Nuclei

⁹⁴

Ru,

⁹⁵

Rh and

¹⁷²

Pt via their Electromagnetic

Properties

AYŞEGÜL ERTOPRAK

Doctoral Thesis in Physics Stockholm, Sweden, 2020

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TRITA-FYS 2020:07 ISSN 0280-316X

ISRN KTH/FYS/–20:07–SE ISBN 978-91-7873-484-9

KTH, AlbaNova University Center SE-106 91, Stockholm SWEDEN Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av Teknologie Doktorsexamen 23 April 2020 kl 14.00 i Sal F3, KTH Campus, Lindstedtsvägen 26, Stockholm.

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iii

Abstract

This thesis reports new results obtained from studies of the neutron deficient atomic nuclei⁹⁴Ru,⁹⁵Rh and¹⁷²Pt using two different experimental set-ups.

In the first part, lifetimes of highly excited states in nuclei near the N=50 closed-shell (⁹⁴Ru and ⁹⁵Rh) were deduced from an analysis of the Doppler broadened transition lineshapes measured following the ⁵⁸Ni(⁴⁰Ca, 4p) and

58Ni(⁴⁰Ca, 3p) fusion-evaporation reactions at the Grand Accélérateur Na- tional d’Ions Lourds (GANIL) accelerator complex situated in Caen, France.

Doppler Shift Attenuation Method (DSAM) lifetime analysis was performed on the Doppler broadened peaks in energy spectra from γ-rays emitted from excited states in the nuclei of interest while they were slowing down in a thick 6 mg/cm² metallic⁵⁸Ni target. For⁹⁴Ru, eight excited-state lifetimes in the angular momentum range I = (13 − 20)~ have been measured in total, five of which were determined for the first time. For the lifetime analysis of ⁹⁵Rh, three lifetime values have been obtained. One of them, the life- time of the 39/2⁻₁ excited state, has been measured for the first time. In the other cases, the lifetimes of the previously measured 29/2⁻₂ and 37/2⁻₁ excited states have been obtained. The corresponding B(M1) and B(E2) re- duced transition strengths have been deduced and are discussed within the framework of large-scale shell model (LSSM) calculations.

In the second part, the extremely neutron deficient¹⁷²Pt nucleus has been studied. Excited states in ¹⁷²Pt were populated using the ⁹⁶Ru(⁷⁸Kr, 2p) and ⁹²Mo(⁸³Kr, 3n) reactions at the Accelerator Laboratory of the Univer- sity of Jyväskylä (JYFL), Finland. Prompt γ-rays were detected using the JUROGAM high-purity germanium detector array at the target position while the identification and decay spectroscopy of ¹⁷²Pt was performed using the RITU gas-filled separator in conjunction with the GREAT spectrometer.

The Recoil Decay Tagging (RDT) technique was used for the selection of prompt γ-rays. The known positive-parity band has been extended and the negative-parity structure has been established on top of the lowest member of the negative parity band which has now been firmly assigned as spin-parity 3⁻. Moreover, the newly observed E3 transition provides a link between the negative parity band with the ground state. The observations of this E3 transition together with several E1 transitions connecting the negative- parity structure with the ground-state band is consistent with the presence of octupole collectivity in¹⁷²Pt. Furthermore, this is the first observation of an E3 transition connecting the negative parity band with the ground-state band in the Pt-Os-W region. The experimental results were interpreted in terms of LSSM and total routhian surface calculations. With the support of these theoretical calculations, evidence for octupole collectivity in¹⁷²Pt is proposed.

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iv

Sammanfattning

Denna avhandling beskriver resultat från studier av de neutronfattiga isoto- perna rutenium-94 (⁹⁴Ru), rodium-95 (⁹⁵Rh) och platina-172 (¹⁷²Pt). Den första delen av avhandlingen behandlar livstidsmätningar för högt exciterade tillstånd i kärnorna ⁹⁴Ru och ⁹⁵Rh med antalat neutroner, N, = 50 vilket motsvarar ett slutet skal i den modell för atomkärnors struktur som benämns skalmodellen. Livstider för⁹⁴Ru och⁹⁵Rh härleddes från en analys av Dopp- lerbreddade övergångslinjer uppmätta efter det att kärnorna skapats i fusion mellan jonstrålar av kalcium-40 och strålmål bestående av nickel-58. Experi- mentet utfördes vid den franska acceleratoranläggningen Grand Accélérateur National d’Ions Lourds (GANIL). Gammastrålning uppmättes med germaniumdetektorsystemet EXOGAM medan elektriskt laddade partiklar och neutroner som utsändes i anslutning till fusionsreaktionerna registrerades i CsI- detektorsystemet DIAMANT respektive neutron detektorsystemet Neutron Wall. För⁹⁴Ru har livstider uppmätts för åtta exciterade tillstånd med spinn i intervallet I = 13−20~. För fem av dessa bestämdes livstiden för första gång- en. För⁹⁵Rh har tre livstidsvärden erhållits. För ett av dem, 39/2⁻₁, har livs- tiden uppmättts för första gången i detta arbete. I de tvä andra fallen (37/2⁻₁ och 29/2⁻₂) var livstiden känd sedan tidigare men har nu uppmätts med högre precision. De reducerade övergångssannolikheterna för magnetiska dipolöver- gångar och elektriska kvadrupolövergångar (B(M1) respektive B(E2)) från dessa tillstånd har härletts från de uppmätta livstiderna samt förgrenings- förhållanden för de relevanta elektromagnetiska övergångarna. Dessa jämförs med och diskuteras inom ramen för storskaliga skalmodellsberäkningar (LS- SM). I den andra delen av avhandlingsarbetet har den extremt neutronfattiga atomkärnan ¹⁷²Pt studerats. Exciterade tillstånd i ¹⁷²Pt populerades i fusionsreaktionerna⁹⁶Ru(⁷⁸Kr, 2p)¹⁷²Pt^∗och⁹²Mo(⁸³Kr, 3n)¹⁷²Pt^∗ mellan jonstrålar av kryptonisotoperna med masstal 78 och 83 och strålmål bestående av tunna folier av rutenium-96 respektive molybden-92. Dessa experiment ut- fördes vid Acceleratorlaboratoriet vid universitetet i Jyväskylä (JYFL), Fin- land. Prompt gammastrålning detekterades med germaniumdetektorsystemet JUROGAM vilket var placerat i anslutning till strålmålet. Sönderfallsspektro- skopi av¹⁷²Pt och andra neutronfattiga fusionsprodukter utfördes i fördröjd koincidens mellan JUROGAM och spektrometern för radioaktiva sönderfall, GREAT efter att de hade passerat den gasfyllda elektromagnetiska rekylse- paratorn RITU. Den s.k. Recoil Decay Tagging (RDT)-tekniken användes för identifiering av de sällsynta¹⁷²Pt-kärnorna. På detta sätt kunde den kända strukturen av exciterade tillstånd i¹⁷²Pt och elektromagnetiska övergångar mellan dessa tillstånd och till grundtillståndet utökas. I synnerhet har ett lågt liggande tillstånd med spin-paritet 3⁻fastställts och sönderfallet mellan detta tillstånd och grundtillståndet observerats. Bl.a. egenskaperna hos denna gammaövergång med multipolaritet E3 stöder teoretiska förutsägelser om att atomkärnan ¹⁷²Pt uppvisar oktupolkollektivitet dvs. kan exciteras från grundtillståndet till ett oktupolvibrationellt tillstånd.

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v

Acknowledgements

Firstly, I am extremely grateful to my supervisor Prof. Bo Cederwall, for giving me the opportunity to be a part of the KTH nuclear physics group. His guidance and scientific support have always been a great source of motivation throughout my PhD. I would like to thank Prof. Roberto Liotta who has helped me not only to improve my knowledge on the nuclear theory but also extremely fruitful discussions related to physics all the time. Many thanks to my co-supervisor Prof.

Ayşe Ataç Nyberg for her help and advice during my studies. I want to thank Prof.

Baki Akkuş for his encouragement and support to be able to continue my work both here and in the Istanbul University simultaneously. I would like to thank Doc. Chong Qi for his contributions to this work with the fantastic theoretical calculations and comments on the papers. Special thanks to Dr. Torbjörn Bäck for interesting physics discussions and also his careful proof-reading this thesis. I would like to thank Prof. Arne Johnson and Prof. Ramon Wyss for their fruitful collaborations. I am also grateful to Dr. Maria Doncel for her positive attitude, advice, and help during my studies. I would like to thank all the group members of nuclear physics at KTH for the relaxed working atmosphere with theoretical and experimental discussions during my PhD. Particular thanks to Özge Aktaş for the friendship throughout the last three years, it was very nice to spend time together in Stockholm. Thank you, my colleagues: Dr. Farnaz Ghazi Moradi, Dr. Hongna Liu, Dr. Ulrika Jakobsson, Dr. Hongjie Li, Dr. Debora Trombetta, Dr. Sara Changizi, Wei Zhang, Xiaoyu Liu, Daniel Karlsson, Karl Sallmén, Linda Eliasson, Cibi Sundaram, Jana Petrovic, Akshay Kishore Kallianpur. I would like to thank the staff at the Grand Accélérateur National d’Ions Lourds (GANIL) accelerator facility in France and at the Accelerator Laboratory of the University of Jyväskylä (JYFL) in Finland for the excellent technical support with enormous help during the experiments and valuable comments for the papers. Many thanks to all my friends who contributed to this work. Especially, I am thankful to my best friends Kübra Özgüvenir and D. Pelin Pat for their enduring friendships, which hold us together for many years even when we were away from each other.

Finally, I would like to express my deepest thanks to my family: my mother Şükran, father İsmail, brother Murat, grandmother Remziye, and auntie Yurdanur.

Thanks for giving me continual encouragement and support. None of this would have been possible without your unwavering love. Special thanks to my dearest grandfather for his inspiration throughout my life and support to pursue my dreams.

I want to thank my Serkan for being there for me with such valuable encouragement throughout this journey and all the great joy he has brought into my life.

Ayşegül Ertoprak, Stockholm, 2020

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List of Publications

This thesis is based on the first four publications in the list below.

1. Lifetime measurements with the Doppler shift attenuation method using a thick homogeneous production target-verification of the method

A. Ertoprak, B. Cederwall, U. Jakobsson, B. M. Nyakó, J. Nyberg, P. Davies, M. Doncel, G. de France, I. Kuti, D. Napoli, R. Wadsworth, S. S. Ghugre, R.

Raut, B. Akkus, H. Al-Azri, A. Algora, G. de Angelis, A. Atac, T. Bäck, A. Boso, E. Clement, D. M. Debenham, Zs. Dombradi, S. Erturk, A. Gadea, F. Ghazi Moradi, A. Gottardo, T. Huyuk, E. Ideguchi, G. Jaworski, H. Li, C. Michelagnoli, V. Modamio, J. Nyberg, M. Palacz, C. Petrache, F. Recchia, M. Sandzelius, M.

Siciliano, J. Timar, J. J. Valiente-Dobon and Z. G. Xiao Acta Physica Polonica B, 48, 325 (2017)

2. M1 and E2 transition rates from core-excited states in semi-magic⁹⁴Ru A. Ertoprak, B. Cederwall, C. Qi, M. Doncel, U. Jakobsson, B. M. Nyakó, G.

Jaworski, P. Davies, G. de France, I. Kuti, D. Napoli, R. Wadsworth, S. S. Ghugre, R. Raut, B. Akkus, H. Al Azri, A. Algora, G. de Angelis, A. Atac, T. Bäck, A.

Boso, E. Clement, D. M. Debenham, Zs. Dombradi, S. Ertürk, A. Gadea, F. Ghazi Moradi, A. Gottardo, T. Hüyük, E. Ideguchi, H. Li, C. Michelagnoli, V. Modamio, J. Nyberg, M. Palacz, C. M. Petrache, F. Recchia, M. Sandzelius, M. Siciliano, J.

Timár, J. J. Valiente-Dobón and Z. G. Xiao EPJ A, 54, 145 (2018)

3. Evidence for octupole collectivity in¹⁷²Pt

A. Ertoprak, B. Cederwall, C. Qi, Ö. Aktas, M. Doncel, B. Hadinia, R. Li- otta, M. Sandzelius, C. Scholey, K. Andgren, T. Bäck, H. Badran, T. Braunroth, T. Calverley, D. M. Cox, D. M. Cullen, Y. D. Fang, E. Ganioglu, M. Giles, M. B.

Gomez Hornillos, T. Grahn, P. T. Greenlees, J. Hilton, D. Hodge, E. Ideguchi, U. Jakobsson, A. Johnson, P. M. Jones, R. Julin, S. Juutinen, S. Ketelhut, A.

Khaplanov, M. Kumar Raju, M. Leino, H. Li, H. Liu, S. Matta, V. Modamio, B. S. Nara Singh, M. Niikura, M. Nyman, I. Özgur, R. D. Page, J. Pakarinen, P.

Papadakis, J. Partanen, E. S.Paul, C. M. Petrache, P. Peura, P. Rahkila, P. Ruot- vii

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viii LIST OF PUBLICATIONS

salainen, J. Saren, J. Sorri, S. Stolze, P. Subramaniam, M. J. Taylor, J. Uusitalo, J. Valiente-Dobon and R. Wyss

EPJ A, 56, 65 (2020)

4. Lifetime measurements of core-excited states in semi-magic⁹⁵Rh

A. Ertoprak, C. Qi, B. Cederwall, M. Doncel, U. Jakobsson, B. M. Nyakó, G.

Jaworski, P. Davies, G. de France, I. Kuti, D. Napoli, R. Wadsworth, S. S. Ghugre, R. Raut, B. Akkus, H. Al Azri, A. Algora, G. de Angelis, A. Atac, T. Bäck, A.

Boso, E. Clement, D. M. Debenham, Zs. Dombradi, S. Ertürk, A. Gadea, F. Ghazi Moradi, A. Gottardo, T. Hüyük, E. Ideguchi, H. Li, C. Michelagnoli, V. Modamio, J. Nyberg, M. Palacz, C. M. Petrache, F. Recchia, M. Sandzelius, M. Siciliano, J.

Timár, J. J. Valiente-Dobón and Z. G. Xiao (To be submitted to EPJ A)

The author has also contributed to the experimental part of the following publications that are not commented in this thesis.

5. Isospin properties of nuclear pair correlations from the level structure of the self-conjugate nucleus⁸⁸Ru

B. Cederwall, X. Liu, Ö. Aktas, A. Ertoprak, W. Zhang, C. Qi, A. Atac Nyberg, T. Bäck, M. Doncel, E. Clement, G. de France, J. Ljungvall, B. M. Nyako, J.

Nyberg, I. Kuti, D. Sohler, J. Timar, G. Jaworski, A. Goasduff, D. R. Napoli, R.

Wadsworth, D. Mengoni, G. de Angelis, A. Gottardo, H. Al-Azri, A. Gadea, M.

Jurado, C. M. Petrache, D. Ralet and J. J. Valiente-Dobon Phys. Rev. Letters, 124, 062501 (2020)

6. Evidence of enhanced octupole correlations at high spins in¹³⁶Nd.

C. M. Petrache, N. Minkov, T. Nakatsukasa, B. F. Lv, A. Astier, E. Dupont, K. K. Zheng, P. T. Greenlees, H. Badran, D. M. Cox, T. Grahn, R. Julin, S.

Juutinen, J. Konki, M. Leino, J. Pakarinen, P. Papadakis, J. Partanen, P. Rahkila, M. Sandzelius, J. Saren, C. Scholey, J. Sorri, S. Stolze, J. Uusitalo, B. Cederwall, Ö Aktas, A. Ertoprak, H. Liu, S. Matta, P. Subramaniam, S. Guo, M. L. Liu, X.

H. Zhou, K. L. Wang, I. Kuti, J. Timár, A. Tucholski, J. Srebrny and C. Andreoiu Submitted to Phys. Letters B, (2020)

7. Highly-deformed bands in Nd nuclei: new results and consistent interpreta- tion within the Cranked Nilsson-Strutinsky formalism

C. M. Petrache, B. F. Lv, A. Astier, E. Dupont, K. K. Zheng, P. T. Greenlees, H.

Badran, T. Calverley, D. M. Cox, T. Grahn, J. Hilton, R. Julin, S. Juutinen, J.

Konki, J. Pakarinen, P. Papadakis, J. Partanen, P. Rahkila, P. Ruotsalainen, M.

Sandzelius, J. Saren, C. Scholey, J. Sorri, S. Stolze, J. Uusitalo, B. Cederwall, Ö Aktas, A. Ertoprak, H. Liu, S. Guo, M. L. Liu, J. G. Wang, X. H. Zhou, I. Kuti, J. Timar, A. Tucholski, J. Srebrny and C. Andreoiu

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ix

Phys. Rev. C, 100, 054319 (2019)

8. Chirality of¹³⁵Nd reexamined: Evidence for multiple chiral doublet bands B. F. Lv, C. M. Petrache, Q. B. Chen, J. Meng, A. Astier, E. Dupont, P. T.

Greenlees, H. Badran, T. Calverley, D. M. Cox, T. Grahn, J. Hilton, R. Julin, S. Juutinen, J. Konki, J. Pakarinen, P. Papadakis, J. Partanen, P. Rahkila, P.

Ruotsalainen, M. Sandzelius, J. Saren, C. Scholey, J. Sorri, S. Stolze, J. Uusitalo, B. Cederwall, A. Ertoprak, H. Liu, S. Guo, M. L. Liu, J. G. Wang, X. H. Zhou, I. Kuti, J. Timar, A. Tucholski, J. Srebrny and C. Andreoiu

Phys. Rev. C, 100, 024314 (2019)

9. Collective rotation of an oblate nucleus at very high spin

C. M. Petrache, S. Frauendorf, B. F. Lv, A. Astier, E. Dupont, S. Guo, M. L. Liu, X. H. Zhou, K. L. Wang, P. T. Greenlees, H. Badran, D. M. Cox, T. Grahn, R.

Julin, S. Juutinen, J. Konki, J. Pakarinen, P. Papadakis, J. Partanen, P. Rahkila, M. Sandzelius, J. Saren, C. Scholey, J. Sorri, S. Stolze, J. Uusitalo, B. Cederwall, Ö Aktas, A. Ertoprak, H. Liu, I. Kuti, J. Timar, A. Tucholski, J. Srebrny and C.

Andreoiu

Phys. Rev. C, 99, 041301(R) (2019)

10. Lifetime measurements of excited states in ¹⁷²Pt and the variation of quadrupole transition strength with angular momentum

B. Cederwall, M. Doncel, Ö Aktas, A. Ertoprak,, R. Liotta, C. Qi, T. Grahn, D.

M. Cullen, D. Hodge, M. Giles, S. Stolze, H. Badran, T. Braunroth, T. Calverley, D. M. Cox, Y. D. Fang, P. Greenlees, J. Hilton, E. Ideguchi, R. Julin, S. Juutinen, M. Kumar Raju, H. Li, H. Liu, V. Modamio, J. Pakarinen, P. Papadakis, J. Parta- nen, C. Petrache, P. Rahkila, P. Ruotsalainen, M. Sandzelius, J. Saren, C. Scholey, J. Sorri, P. Subramaniam, M. J. Taylor, J. Uusitalo and J. J. Valiente-Dobon Phys. Rev. Letters, 121, 022502 (2018)

11. Evolution from γ-soft to stable triaxiality in¹³⁶Nd as a prerequisite of chirality

B. F. Lv, C. M. Petrache, A. Astier, E. Dupont, A. Lopez-Martens, P. T. Green- lees, H. Badran, T. Calverley, D. M. Cox, T. Grahn, J. Hilton, R. Julin, S. Juu- tinen, J. Konki, M. Leino, J. Pakarinen, P. Papadakis, J. Partanen, P. Rahkila, M. Sandzelius, J. Saren, C. Scholey, J. Sorri, S. Stolze, J. Uusitalo, A. Herzan, B.

Cederwall, A. Ertoprak, H. Liu, S. Guo, M. L. Liu, Y. H. Qiang, J. G. Wang, X.

H. Zhou, I. Kuti, J. Timar, A. Tucholski, J. Srebrny and C. Andreoiu Phys. Rev. C, 98, 044304 (2018)

12. Evidence of chiral bands in even-even nuclei C. M. Petrache, B. F. Lv, A.

Astier, E. Dupont, Y. K. Wang, S. Q. Zhang, P. W. Zhao, Z. X. Ren, J. Meng, P.

T. Greenlees, H. Badran, D. M. Cox, T. Grahn, R. Julin, S. Juutinen, J. Konki,

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x LIST OF PUBLICATIONS

J. Pakarinen, P. Papadakis, J. Partanen, P. Rahkila, M. Sandzelius, J. Saren, C.

Scholey, J. Sorri, S. Stolze, J. Uusitalo, B. Cederwall, Ö. Aktas, A. Ertoprak, H.

Liu, S. Matta, P. Subramaniam, S. Guo, M. L. Liu, X. H. Zhou, K. L. Wang, I.

Kuti, J. Timar, A. Tucholski, J. Srebrny and C. Andreoiu Phys. Rev. C, 97, 539 (2018)

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List of Figures

1.1 Relevant parts of the nuclide chart showing the studied nuclei in the present work. (a) Neutron deficient nuclei studied near the N = Z = 50 region. ⁹⁴Ru and⁹⁵Rh are highlighted in green and pink, respectively.

The stable nuclei are indicated by grey while the proton Z = 50 and neutron N = 50 shell closures are highlighted in blue. (b) The studied extremely neutron deficient nucleus (¹⁷²Pt), located close to the proton drip line (orange), is shown in blue. . . . 4 2.1 Shell model orbitals important for the description of nuclei in the region

around¹⁰⁰Sn, and single particle energies (SPE) relative to¹⁰⁰Sn. The SPE values given in the right-hand part of the figure are in MeV. The differences between the values for protons and neutrons are mainly due to the electromagnetic repulsion between protons. Levels representing the SPE energies are plotted symmetrically with respect to the centre of the N = 50 and Z = 50 shell gaps. . . . 8 2.2 TRS plots in the β2− β3 coordinate system for the vacuum (ground-

state) configuration (left) and the lowest negative-parity configuration (right) in neutron deficient ¹⁷²Pt nucleus. The red dot denotes the position of the ground-state minimum. The contours below 6 MeV are displayed, and the energy difference between neighbouring contours is 200 keV. . . . 9 3.1 Schematic representation of the⁵⁸Ni(⁴⁰Ca,xnyp) fusion-evaporation re-

action. . . 14 3.2 Left: Photograph of the EXOGAM Ge-array (right side of the yellow

support frame) and the Neutron Wall detector array (left side). The beam enters via a vacuum pipe from the right, striking the target which is mounted at the centre of the detection system, see also 3.5. Right:

Close-up photograph of the EXOGAM detectors taken with the Neu- tron Wall and the downstream hemisphere of the target chamber and beamline retracted. An empty target frame is mounted at the centre of the target chamber (Photos by B. Cederwall). . . 15

xiii

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xiv List of Figures

3.3 Left: Neutron Wall seen from downstream the target, here consisting of 50 liquid scintillator detectors. Right: DIAMANT detector array (Photos by A. Ertoprak). . . 16 3.4 A schematic drawing of the DIAMANT detector array (courtesy of

B. M. Nyakó) . . . 17 3.5 A schematic drawing of the GREAT+RITU+JUROGAM detector set-

up (from left to right) at the University of Jyväskylä. (Courtesy of D.

Seddon, University of Liverpool.) . . . 19 3.6 Schematic view of the gas-filled recoil separator RITU. The strongly

focusing quadrupole magnets are denoted by Q1, Q2, Q3 and the dipole magnet for bending particles is denoted by D. . . 20 3.7 Schematic drawing of decay spectroscopy using the GREAT spectrometer. 22 4.1 Basic principle behind the Doppler Shift Attenuation Method for lifetime

determinations of short-lived nuclear states. Due to the slowing down of the fusion products in the target, the velocity at which the γ-rays from excited states are emitted (magenta, blue, and red, respectively) decreases on average with the emission time. . . 26 4.2 Experimental fusion excitation function for the ⁴⁰Ca +⁵⁸Ni reaction,

taken from D. Bourgin et al. . . 28 4.3 The intrinsic asymmetry of the peak shape for completely stopped 756 keV

γ-ray transition. . . 32 4.4 Detailed view of the level scheme of ⁹⁴Ru obtained from the present

work. Levels with measured lifetime are highlighted in blue. . . 33 4.5 Experimental γ-ray energy spectra and fits to the Doppler shifted shapes

for the 1898 keV (13⁺1 → 12⁺1) transition in ⁹⁴Ru. The spectra were produced by setting a narrow gate on the stopped component of the 725 keV transition decaying from the 4717 keV state in the Eγ₁− Eγ₂

coincidence matrix. Here Eγ₁refers to energies of γ-rays detected at 90^◦ or 135^◦ with respect to the beam direction while Eγ₂ refers to energies of any γ-rays detected in coincidence with these γ-rays. . . 34 4.6 Angular Distribution Ratio RAas a function of energy from the present

work. . . 38 4.7 Schematic drawing of the principle of linear polarization measurement

of γ-rays emitted from polarized nuclei. . . 40 4.8 Deduced polarization asymmetry parameter (A) versus angular distri-

bution ratio (RA) of γ-ray transitions. The horizontal line divides the regions of polarization asymmetry into two as positive and negative, which defines if the corresponding transition is electric or magnetic. . . 41

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List of Figures xv

5.1 Comparison between the experimental and theoretical transition strengths for M1 and E2 transitions in⁹⁴Ru. The top panel shows B(M1) values and the bottom panel gives the B(E2) values. The transition labels show the assigned initial and final states for the transitions. Experimental values are marked by circles with error bars. See text for details. . . 45 5.2 Combined coincidence γ-ray energy spectrum obtained by the sum of

the gates on the 374, 662 and 213 keV transitions in the RDT-selected Eγ− Eγ matrix. . . 48 5.3 Level scheme of ¹⁷²Pt deduced from the present work. The new tran-

sitions are highlighted in blue. Transition energies are given in keV.

Tentative spin-parity assignments are given in parenthesis. The arrow thickness indicates the relative intensity of the transitions. . . 49 5.4 Comprehensive B(E1) systematics of known nuclei in the Pt-Os-W re-

gion (168 ≤ A ≤ 178) as a function of initial angular momentum. . . 50

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List of Tables

2.1 Reduced Transition probabilities (B(EL) and B(ML)) and Partial Tran- sition probabilities (λ(EL) and λ(ML)) are listed for the first three electric and magnetic multipoles, respectively. Energy, E, is given in MeV. A is the nuclear mass number (baryon number). . . 11

4.1 Production cross section as a function of target depth, divided into ten bins, the ten thickness boundaries for defining the bins and the relative yield in each bin. The cross section, beam energy in the centre of mass frame, and the laboratory frame are given in the first, second and third column respectively. The target thickness boundaries are given in column 4. . . 29 4.2 Peak asymmetries fitted for selected γ-ray transitions in⁹⁴Ru, see text.

The spin-parity assignments and γ-ray energies are given in the first and second column, respectively. The Beta parameter values (Beta is the skewness parameter for the skew Gaussian component and varies slowly with γ-ray energy) are shown in the column 3. Previous lifetime values or limits for the initial state are given in the column 5. The smooth step function components were fixed to zero during the fitting procedure.

Uncertainties are given within parentheses. The asymmetry parameter R is found to be constant around R = 15 for peaks corresponding to transitions known to occur when the nuclei are at rest in the target, while transitions from states which have previously been reported by Jungclaus et al. to have short lifetimes of the order of picoseconds and no slow feeding systematically have R values of 20 and higher. . . 30 4.3 Relative γ-ray intensities for ⁹⁴Ru measured in the present work. . . 36

5.1 Lifetimes of excited states in⁹⁴Ru from the present work in comparison with previously reported values and limits. . . 44

xvi

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List of Tables xvii

5.2 Lifetimes of the negative-parity states in ⁹⁵Rh obtained in this work.

The initial level excitation energy (Ex), spin-parity assignments and γ-ray transition energy (Eγ) are given in the first, second, and third column, respectively. Lifetime values, τ, extracted from the present work are presented in column 4. The corresponding lifetime results reported by Jungclaus et al. are shown in column 5. The experimental reduced transition probabilities B(M1) and B(E2) values which were extracted from the present lifetime measurements, branching ratios are given in column 6 and 7, respectively. . . 44

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List of Acronyms

BGO bismuth germanate

CsI caesium iodide

DSAM Doppler Shift Attenuation Method

EM electromagnetic

FWHM full width at half maximum

GANIL Grand Accélérateur National d’Ions Lourds

ho harmonic oscillator

HPGe high-purity germanium

LSSM large-scale shell-model

QCD quantum chromodynamics

QED quantum electrodynamics

RDT recoil decay tagging

RDDS recoil distance Doppler shift SPE single particle energies

SRIM Stopping and Range of Ions in Matter

TOF time-of-flight

TRS total routhian surface

ZCO zero-crossover

WS Woods-Saxon

xix

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Chapter 1

Introduction

Nuclear physics research aims to achieve a better understanding of the structure and dynamics of atomic nuclei. The atomic nucleus is an extremely complex system of strongly interacting protons and neutrons. Such systems constitute more than 99.9% of the mass of the “ordinary” matter of the Universe (which, incidentally, is only a relatively small fraction of its total mass-energy; the missing mass and energy is called dark matter and dark energy, respectively). In the 1960s and 70’s a theory emerged that could explain the origin of the strong force acting within hadrons, i.e. between the constituent quarks. That is Quantum Chromo Dynamics (QCD) [1]. Nucleons are not the elementary particles that they were thought to be before QCD was invented. As is now well known, a nucleon consists of quarks and gluons.

The quarks are the elementary particles interacting via the strong force (as well as the electromagnetic and weak forces) in the Standard Model, and they are massive fermions. The gluons are massless bosons that transmit the strong force, binding quarks together. From a nuclear physics viewpoint, the most important drawback of QCD is that it is not known how to solve exactly the QCD equations of motion regulating the motion of quarks. The only first-principles approach available is to attempt to solve the equations numerically, using what is called lattice QCD.

This requires complicated algorithms and very powerful computers. However, the most complicated system that could be solved in this fashion is currently just a free nucleon. It is for this reason that the modelling of low-energy nuclear properties is performed by means of effective forces which are easier to apply and may still explain some nuclear features with reasonable accuracy. The first of such features is that the nuclear force is of a very short range and nucleons inside a nucleus move following relatively long mean free paths. In other words, in a first approximation one may consider the dynamics of nucleons inside a nucleus as that of free spin 1/2 particles obeying the Pauli principle (this is called a Fermi gas). Since the nucleons are tightly bound inside the nucleus the most simple assumption is to consider the free nucleons moving inside a schematic potential like a square well (as a function of the radius from the centre of the nucleus) or, more realistically, inside a harmonic

1

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2 CHAPTER 1. INTRODUCTION

oscillator or Woods-Saxon potential. This is the basis of the nuclear shell model.

Within this extremely simple picture, it was possible to explain the lowest of the so-called “magic” numbers which are discussed in the following section.

After the discovery of the nuclear shell model [2, 3], experimental research has extended more and more into the realm of exotic nuclei, far away from the valley of β stability and close to the proton or neutron drip lines. One of the major find- ings obtained in recent years is that nuclear shell structure evolves as a function of isospin and that even the “magic numbers” change far from stability [4]. Therefore, experimental techniques, e.g. used in γ-ray spectroscopy, are evolving to obtain in- formation about nuclei at the extreme regions of the Segré chart. With the help of fusion-evaporation reactions, the possibility to observe the neutron deficient nuclei, especially for nuclei in the range of N > Z, has been increased. To be able to reach the desired neutron deficiency, evaporation of neutrons from the compound nucleus (which is typically already neutron deficient) is mandatory, resulting in very low cross-sections. Furthermore, the emission of charged particles, neutrons and γ-rays in reactions leading to the nuclei of interest are observed in a vast background from the prolific reaction channels leading to residual nuclei close to stability. This requires more sensitive experimental techniques. One of those experimental techniques used in the present work is called Recoil Decay Tagging (RDT) which aims to select cleanly the nuclei of interest using the characteristic decay properties of the residual nucleus. By using a highly segmented HPGe detector array in conjunction with a recoil separator and a focal plane decay spectrometer, the structure of those nuclei and the information about their decay properties can be extracted. As we approach the most neutron-deficient nuclei, the alpha-emission branching ratios are increasing. Taking advantage of short half-lives together with the information from the characteristic decay properties such as α-decay allows us to perform the prompt spectroscopy correlated with focal plane decay spectroscopy by using this technique. The extremely neutron-deficient nucleus¹⁷²Pt is located just below the proton magic number Z = 82 and ∼ 20 neutrons far away from the closest stable platinum isotope which is ¹⁹⁰Pt.

The heaviest self-conjugate doubly-magic nucleus¹⁰⁰Sn and the neighbouring nuclei around the N = Z line provide an excellent ground for testing state-of-art theory. Moreover, in these nuclei neutrons and protons occupy similar orbitals, enhancing the neutron-proton interactions leading to increased importance of such correlations. However, such nuclei are populated in nuclear reactions with very small cross-sections, which needs to be overcome with the usage of HPGe detector arrays, such as EXOGAM, coupled to efficient ancillary detectors for the large selection of evaporated particles and reaction products, such as DIAMANT and Neutron Wall. Besides experimental investigations of nuclei near ¹⁰⁰Sn, many theoretical models have been developed to test the feasibility of the shell model in this specific region of the nuclear chart, especially the heavy N = 50 isotones. In this region, the nuclear shell model produces the main structural features of low-lying states by using a model space consisting of an inert core including the 0g9/2 and 1p1/2 subshells while also taking into account particle-hole excitations by adding

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3

particles (or holes). Core excited states, which are produced by breaking the core via particle excitations across a major shell gap, here become important above I ≈ 12~, and have been observed in several nuclei of this region [5–8]. Due to the large model space, performing theoretical calculations in this region is very challenging but is progressing due to advances in supercomputer performance. Electromagnetic decay properties such as transition probabilities and branching ratios, which can be extracted from the lifetime measurements, and relative γ-ray intensities enable us to test the state-of-the-art theory stringently and systematically across the major shell gap at N = 50.

This doctoral thesis presents studies of the neutron deficient atomic nuclei

94Ru,⁹⁵Rh, and¹⁷²Pt, see Fig. 1.1. They have been produced in fusion-evaporation reactions using accelerated heavy ion beams and stable targets from the accelerator facilities Grand Accélérateur National d’Ions Lourds (GANIL), France and Accelerator Laboratory of the University of Jyväskylä (JYFL), Finland. In the first research subject of this thesis, we focused on the measurement of lifetimes of medium-high-spin states in the semi-magic¹ nuclei (N = 50)⁹⁴Ru and⁹⁵Rh using a modified version of the Doppler Shift Attenuation technique. The results were compared with large-scale shell model (LSSM) calculations. Previously reported lifetime values from an independent measurement have been validated with this new technique which utilises thick homogeneous production targets. This resulted in paper I, II and IV. The second research subject contains a detailed spectro- scopic study of the extremely neutron deficient nucleus¹⁷²Pt. The observation of an E3 transition together with several E1 transitions connecting the negative-parity band with the ground state band constitutes evidence for octupole collectivity in

172Pt (paper III). The effect is somewhat unexpected since ¹⁷²Pt is situated in a region of the nuclear chart which is relatively far away from the neutron and proton numbers normally associated with strong octupole correlations. The results have been discussed in the framework of large-scale shell-model and total routhian surface calculations which supports the idea of octupole collectivity in¹⁷²Pt.

The doctoral thesis is grouped into six chapters: following the introduction section, Chapter 2 provides the theoretical background for the relevant information in nuclear structure theory. Chapter 3 contains the experimental details which include the reaction mechanisms and the experimental set-ups used to populate excited states of the neutron deficient nuclei studied in the present work. Chapter 4 describes the experimental techniques that have been used to extract the information from the experimental data during the data analysis. Chapter 5 presents experimental results that are obtained from the present work and their interpreta- tion in the frame of theoretical models. Chapter 6 gives a summary of the papers (papers I, II, III and IV)resulting from the present study and the contributions to these papers from the author.

1“Semi-magic” here means that the neutron number N = 50 is “magic” (while the proton number, Z, is not), and hence the nucleus should exhibit a special structure that is easier to describe theoretically and therefore is a good testing ground for theoretical models such as the nuclear shell model, in particular with respect to core-excited states.

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4 CHAPTER 1. INTRODUCTION

Figure 1.1: Relevant parts of the nuclide chart showing the studied nuclei in the present work. (a) Neutron deficient nuclei studied near the N = Z = 50 region.

94Ru and ⁹⁵Rh are highlighted in green and pink, respectively. The stable nuclei are indicated by grey while the proton Z = 50 and neutron N = 50 shell closures are highlighted in blue. (b) The studied extremely neutron deficient nucleus (¹⁷²Pt), located close to the proton drip line (orange), is shown in blue.

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Chapter 2

Theoretical Framework

This chapter presents the physics background of the present work from the theoretical point of nuclear structure. The nuclear shell model and shell model parameters are discussed and total routhian surface calculations are introduced.

2.1 Nuclear Shell Model

Properties of atomic nuclei, such as the increase in nucleon separation energies for nuclei with specific number of nucleons, reveal that nuclei with proton or neutron numbers equal to 2, 8, 20, 28, 50, 82, 126 are more stable than predicted by the Bethe-Weizsäcker semi-empirical mass formula [9] also known as the quantum liquid drop model. Already referred to above, these numbers are known as

“magic” numbers and their existence is one of the strongest motivations for the development of the shell model concept.

The Hamiltonian of a bound many-body system such as the atomic nucleus can be written as:

H = T + V =

A

X

k=1

Ti+X

i6=j

Vij, (2.1)

where Ti describes the kinetic energy of each constituent nucleon and Vij describes the interaction between nucleons. Three-body interactions and higher-order interactions between the nucleons are here neglected. Assuming that a central single- particle field U exists so that H = T + U + v with v = V − U is a small (residual) interaction and H0= T + U a pure single-particle Hamiltonian, Eq. 2.1 becomes,

H = H0+ v. (2.2)

The single-particle nuclear shell model assumes that neutrons and protons move under the influence of H0, obeying the Pauli exclusion principle [10]. The corre- sponding nuclear wave function, that is the wave function of the A free nucleons in

5

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6 CHAPTER 2. THEORETICAL FRAMEWORK

the nucleus, is the antisymmetrised product of all the A independent-particle eigen- states. This ensures that the nuclear wave function obeys the Pauli principle as it should for a system of fermions. It is a “Fermi gas”. The central potential H0is often taken to be a harmonic oscillator (ho) potential. With appropriate choice of the parameters defining the ho potential one can describe the lowest magic numbers, as already mentioned.

A potential which more realistically follows the known nuclear density distribution than the ho is the Woods-Saxon potential (WS) [11] which has the form,

V^W.S.(r) = −V0[1 + exp(r − R0

a )]⁻¹. (2.3)

Here, r = |r| is the absolute value of the radius vector from the origin centred at the nuclear centre of mass and hence Eq. 2.3 describes a spherical potential. But even with the WS potential only the lowest magic numbers can be explained. Already in the 1940s, it was found that in order to account for all the known magic numbers one has to include a spin-orbit potential of the form f(r)~l·~s, as was proposed by Goeppert-Mayer and Jensen [2] and for which they received the Nobel Prize in Physics in 1963 (together with Wigner). Nearly simultaneously the shell model was also introduced by Haxel, Jensen and Suess [3].

The disadvantage of using the Woods-Saxon potential and other “realistic” po- tentials is that, in contrast to the ho potential, the single-particle wave functions can not be derived analytically. However in both cases one can characterize the orbits by the quantum numbers n, l, j; i.e. the principal quantum number, the orbital angular momentum and the total angular momentum j = l + s, s being the nucleonic spin. The spin-orbit coupling term splits the levels according to j = l ± 1/2, which presses down high-j and lifts up low-j spin-orbit partners [10].

This “single-particle” shell model now reproduces all the known magic numbers correctly. Besides predicting the correct magic numbers, the shell model also correctly predicts the spins and parities of many excited states in nuclei across the Segré chart. However, in recent years it has become clear that magic numbers (i.e. large shell gaps) can disappear and appear as we move far away from the beta stability line in the nuclear chart, into unexplored territory [4].

When many valence particles (i.e. particles outside the magic core) are con- tained in a nucleus, then the full shell-model Hamiltonian (2.2) including proper residual interaction vhas to be solved. A large number of such effective interactions have been developed during the last decades and it is one of the tasks of modern nuclear theory to better capture the essential physics of the nucleon-nucleon interaction into effective residual forces in large scale shell model calculations.

The spherical shell model works well at predicting nuclear properties for a select group of nuclei which are near closed shells. Nuclei near closed shells generally do not have enough valence particles to facilitate collective motion at low energies, and their structure can be interpreted in terms of single particle excitations. As valence nucleons are added, the shell model wave functions become complicated and are more difficult to model. As indicated above, the simple shell model was developed

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2.1. NUCLEAR SHELL MODEL 7

with a spherically symmetric potential. The expected energy levels corresponding to the solutions of the Schrödinger equation for such a system would shift if the shape of the potential is changed.

Exotic, proton-rich nuclei form a “laboratory” in which many aspects of nuclear structure can be tested. As the neutron deficient nuclei very close to the N = Z line contain similar numbers of protons and neutrons, the two kinds of nucleons are placed in similar or identical states, i.e. “orbitals” within the shell model framework. Hence, their spatial wave functions to a large extent overlap, leading to simplifications and interactions which often cannot be observed in other parts of the nuclide chart. Especially interesting are the studies of nuclei in the vicinity of double closed shells, so-called doubly-magic nuclei, in which the observable properties can be interpreted as a result of the motion of a few valence particles situated outside a more or less inert, “magic”, core. In a first approximation the valence particles can be regarded as moving independently, to second order they interact with each other via residual two-body interactions, and to third order possible excitations of the core are included. The interplay of such single-, two-, and many-body effects studied in the relatively speaking “simple objects” that constitute nuclei with just a few valence particles provides rich opportunities to stringently test nuclear models.

At the crossing points of the N = Z line with the major shell closures, particularly interesting regions of the nuclear chart appear. The arguably most interesting such region is that around the doubly-magic nucleus ¹⁰⁰Sn, which is the heaviest self-conjugate, doubly-magic nucleus that is bound.

2.1.1 Shell model parameters in the ¹⁰⁰Sn region

In order to further our understanding of nuclear structure in the vicinity of¹⁰⁰Sn, a wealth of experimental information on excited states of nuclei in this region should be collected and compared with theoretical model calculations. This will enable verification of the fundamental parameters of the model: the single particle energies (SPE) and residual interactions between valence nucleons. The shell model orbitals important for the description of nuclei in the region of¹⁰⁰Sn are presented in Fig. 2.1. A recent review of the experimental and theoretical achievements in the region has been published in Ref. [12].

Due to the rapid increase in the performance of modern supercomputers, it is gradually becoming possible to model excitations extending beyond the standard shell model valence space with a¹⁰⁰Sn core. One may even investigate directly the N= Z = 50 shell gaps by calculating the properties of “core excited” states at high excitation energy and comparing with their experimental properties.

Recent results on excited states in⁹⁶Pd and⁹⁷Ag [6,13] as well as on E1 transi- tions in the N = 50 isotones⁹⁴Ru [14] and⁹⁵Rh [15] illustrate how this is possible and indicate that the odd-parity orbitals 1p3/2and 0f5/2 couple to the excitations of the doubly-magic N = Z = 50 core, and are necessary for the description of core-excited states.

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8 CHAPTER 2. THEORETICAL FRAMEWORK

Figure 2.1: Shell model orbitals important for the description of nuclei in the region around¹⁰⁰Sn, and single particle energies (SPE) relative to¹⁰⁰Sn. The SPE values given in the right-hand part of the figure are in MeV. The differences between the values for protons and neutrons are mainly due to the electromagnetic repulsion between protons. Levels representing the SPE energies are plotted symmetrically with respect to the centre of the N = 50 and Z = 50 shell gaps.

2.2 Total Routhian Surface (TRS) calculations

In this study, total Routhian Surface (TRS) calculations [16–18] were performed, in addition to the previously mentioned LSSM calculations, to interpret the experimental results. The calculations start from a deformed shell model calculation [19], based on a Wood-Saxon potential [11]. They are designed to calculate the evolution of nuclear shapes and structure as the rotational excitation of a deformed nucleus proceeds to higher rotational frequencies. This is originally called the cranked shell model [20] and reduces dramatically the model space that would be required in a full-scale shell model calculation. In the TRS model, the total energy in the rotating frame, the routhian function, is calculated for a given rotational frequency, ω, as a function of the deformation parameters β2, β3and γ [21]. The energy levels deduced from the experimental work are compared with the minima in the corresponding TRS plot as a function of rotational frequency.

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2.2. TOTAL ROUTHIAN SURFACE (TRS) CALCULATIONS 9

The total routhian of a nucleus with the number of protons (Z) and number of neutrons (N) at rotational frequency ω can be defined as:

E^ω(Z, N, ˆβ) = Emacr^ω (Z, N, ˆβ) + δEshell^ω (Z, N, ˆβ) + δEpair^ω (Z, N, ˆβ), (2.4) where the first term is the macroscopic liquid drop energy, the second and third terms are shell correction energy and pairing correction energy, respectively. ˆβ denotes the deformation parameters (β2, β3 and γ). In an alternative way, Eq. 2.4 can also be written as:

E^ω(Z, N, ˆβ) = E^ω=0(Z, N, ˆβ) + [hΨ^ω| H^ω|Ψ^ωi − hΨ^ω=0| H^ω|Ψ^ω=0i]. (2.5) In Eq. 2.6, the first term (Emacr^ω=0(Z, N, ˆβ)) consists of the liquid drop and shell correction and pairing energies which are extracted using the Strutinsky’s shell correction method at zero frequency [22]. The last term within brackets represents the energy change due to rotation. The total routhian, E^ω(Z, N, ˆβ), is then calculated for corresponding shape parameters to get the equilibrium deformations. The calcu- lated energy values are plotted in a two dimensional x-y-frame (X = β2cos(γ +30^◦) and Y = β2sin(γ + 30^◦)). In the TRS plot, the position of the energy minimum provides information on the favoured deformation.

0 0.1 0.2

3 0

0.05 0.1 0.15 0.2 0.25

2

0 0.1 0.2

3 0

0.05 0.1 0.15 0.2 0.25

2

-5 -4 -3 -2 -1 0 1 2 3 4 5 6

E (MeV)

Figure 2.2: TRS plots in the β2− β3 coordinate system for the vacuum (ground- state) configuration (left) and the lowest negative-parity configuration (right) in neutron deficient¹⁷²Pt nucleus. The red dot denotes the position of the ground- state minimum. The contours below 6 MeV are displayed, and the energy difference between neighbouring contours is 200 keV.

Experimental Studies of the Neutron Deficient Atomic Nuclei 94Ru, 95Rh and 172Pt via their Electromagnetic Properties: Du som saknar dator/datorvana kan kontakta Pär Olsson, polsson@kth.se för information