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G. Georgiev1, G. de France1, F. de Oliveira Santos1, M. Lewitowicz1, I. Matea1, P.F. Mantica2, T.J. Mertzimekis2, T. Glasmacher2, A. Gade2, W.F. Mueller2, L. Weissman2, G. Neyens3, P. Himpe3, D. Yordanov3, N. Vermeulen3, D.L. Balabanski4,5, G. Lo Bianco5,

A. Saltarelli5, Yu.E. Penionzhkevich6, M. Hass7, G. Goldring7, B.S. Nara Singh7, J.M. Daugas8, V. Meot8, H. Grawe9, A. Blazhev9, M. Pfützner10, M. Sawicka10,

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ÄÆÅÈÇCÉ�Ê&Ë#Ì�Ê�ÍÏÎ�Ð�Ë#Ñ�Ò�Ð�Ë#Î�ÓCÔNuclear magnetic moments provide highly sensitive probes to the intrinsic structure of the nuclei and can serve as a stringent test of nuclear models. Especially interesting are their values in the vicinity of shell closures, where the nuclear wave functions are expected to be rather pure. This should manifest itself as the experimental g factors being very close to the single-particle limits (Schmidt lines), corrected by the average standard quenching gs

eff = 0.7 gsfree.

The presence of a sub-shell close is an issue on which many experimental and theoretical works has been devoted in the last few years. According to Ref. [2,3] the structure around 68Ni can be understood in terms of simple configurations implying a sub-shell closure. On the other hand there is no clear effect in the two-neutron separation energies [4], which was explained by quadrupole shape correlations [5]. O. Sorlin et al. [6] state that the shell closure is washed out by pair scattering. The observed collectivity in the Zn [7] and Fe isotopes [8] shows that the closure disappears if one moves just 2 protons above or below the Ni chain. K.H. Langanke et al. [9] question the shell closure at N=40 saying that the E2 strength is distributed mainly within states lying above 4 MeV and it is not exhausted by the first 2+ state in 68Ni. Under these conditions a g-factor measurement of states, with predominant neutron g9/2 components in their wave functions, can probe their single-particle properties and shed light on the structure in the region.

In the Ni isotopes around the N = 40 there are three isomeric states, namely 67mNi (Ex = 1007 keV, t1/2 = 13.3 Õ s), 69mNi (Ex = 2701 keV, t1/2 = 0.44 Ö s) and 70mNi (Ex = 2860 keV, T1/2 = 0.23 × s), whose characteristics are suitable for a g-factor measurement. All of these three isomers are interpreted as having a dominant contribution of the g9/2 neutrons in their structure [10]. This should lead to rather similar values of their g factors. The isomeric states of 67Ni (one valence neutron on g9/2, I Ø = 9/2+) and 70Ni (two valence neutrons on g9/2 coupled to the maximum spin I Ù = 8+) should exhibit similar moments, if their structure is correctly understood (Fig. 1). The isomeric state in 69Ni is expected to have the configuration of two neutrons on g9/2 (I Ú = 8+), coupled additionally to a p1/2 or an f5/2 neutron, giving a total I Û = 17/2-. Comparison of the experimental g factors among each other and to shell model calculations should clarify whether the isomers have the proposed rather pure configurations (thus Z=28 and N=40 being good shell closures), and whether they all have similar configurations, based on the g9/2 neutrons, as suggested.

Ü:Ý Þ�ßVà ß�áJâ�ã�ä åçæèã�é�â�êgâ�æ�ë2ì:í#é�â:î�ÝïÝ æ&ë�êJâ�ð&æ�ñ.à�ò ó�à�àô�ß

There is an accepted proposal at the Tandem of IPN Orsay, France to measure the gyromagnetic factor of the 9/2+ isomeric state in 65Ni. A (d,p) reaction will be used in order to populate the isomer. This is the last 9/2+ isomeric states in the Ni isotopes, which is accessible using stable beams and its half-life (~25ns) does not allow its measurement in projectile fragmentation. The experiment is to be scheduled in the spring of 2004. The g factor of 65mNi (3 neutrons below N=40), together with the presently proposed measurement of 69mNi and 70mNi, respectively 1 and 2 neutrons above N=40, should give a complete picture of the single-particle structure of the Ni isotopes across the proposed 40 sub-shell gap. Each of these experimental values is indispensable for a better understanding of the nuclear structure around 68Ni. They should also help us interpret the rather large deviation of the 67mNi g factor from the systematic in the region (see Fig.2).

õ�ö ÷�ø ù ø úüû0ý�þQÿö �Èþ���� ��� � �����þQÿ �Qþ��±÷�������� � ÿ ������� þ���� ÿ ���±÷���� ��� � !� "���# $%� &�"(' "*)+# ,�$% �' ,�-!$�.�/1032�4!5Here we propose to measure, under the same conditions, the g factors of the isomeric states in 67Ni, 69Ni and 70Ni. This will decrease the systematic uncertainties of the measured values and will allow their direct comparison, independently on any external factors like magnetic field, implantation properties etc.

6+7+8:9+;=<?>?@BAC<?D=EGF+HIAJ<?EGK=LNMOF+D=MOP�<?EGQ=;The method, which we will apply for this measurement, is the Time Dependent Perturbed Angular Distribution (TDPAD) [12]. In projectile-fragmentation reaction one can obtain spin-aligned ensemble of nuclei, provided that the wing of the momentum distribution is selected by the spectrometer (see Fig. 3). Applying a constant magnetic field causes the rotation of the ensemble with the Larmor frequency

RSTVUW XY[Z

, (1)

which is directly proportional to the gyromagnetic factor of the nuclear state and to the applied field. This rotation can be observed as oscillations in the exponential decay of the isomeric state. Positioning \ -ray detectors at 90° with respect to each other and taking the ratio of their difference, divided by their sum, gives the R(t) function

)(2cos4

3

),2/(),(

),2/(),()(

22

22 ]^_`__`__ aabcbb

bac defef

dgdgdgdgdh i

(2)

from which one can derive directly the g factor of the nuclear state. The TDPAD method is a technique which has been widely used in fusion-evaporation reactions [12]. Its application on nuclear states produced in projectile fragmentation leads to some modifications and specific

features, e.g. the usage of the heavy ion – j correlation and the dependence of the spin orientation at the implantation point on the g factor of the isomeric state. A more detailed discussion of the subject can be found in Ref. [1].

In an experiment, performed in December 2002 at GANIL, France, we applied the TDPAD technique in order to measure the g factor of 61mFe and 54mFe, using the fragmentation of 64Ni beam on 9Be target [13]. An example R(t) function form this experiment together with a comparison of the observed experimental alignment to model estimations is presented on Fig.3.

kNl m+n�o�n�pNqsr tvu�w�x�y�r l z�x(u�z�{|r }�~���������~���r { ��x�� l r l z�x�z�u��B�����N��� ��� ������� ���J���1� ��������������� ������� � � � � ����� � �����s  � ��� ¡£¢¤ ��� ��� ¥����%�*¦�§+��� � ������� ¨� ?¨�  � �+�!�������?����� ���(�!��©�  ��¨�����§+� �%����� ������  �(©�����§+¨�� ���%� �%�v������ �§+� ����� ©�� � �������s� � �+��� ¡£¢In the currently proposed experiment the isomers of interest will be produced and spin-aligned following the fragmentation of a 76Ge beam of 130 MeV/u on a 376 mg/cm² Be target. The A1900 fragment separator will be used to select the nuclei of interest. A 300 mg/cm² Al wedge will be used in order to purify the secondary beam. The fully stripped ions will be stopped in a perturbation free implantation host (cubic lattice crystal), positioned between the poles of the electromagnet of the ª -NMR apparatus. It will provide a constant magnetic field in vertical direction. The Larmor precession of the spin-aligned nuclear ensemble will be monitored by 4 SeGA detectors working in "single-crystal" mode. They will be positioned in the horizontal plane at angles ± 45° and ± 135° with respect to the secondary beam. For this purpose a support for the 4 detectors will have to be built. A thin plastic scintillator detector, positioned in the secondary beam just in front of the electromagnet, will be used to give the "t=0" signal for the time-decay curves. The implantation host will be positioned in a vacuum chamber (see Fig. 4) which is presently existing and available.

«N¬ ­+®�¯�®!°�±�²�³�´�µ�¶ ¬ ±(·�¸ µ�¹�¬ º�­¼»�½�¶ ²�³(³*¾�¿+³�¸ ¬ ´�³�º�¶ µ�À?Á ³�¶ Â�¿

Ã+ÄÆÅ:Ç?È+ÉËÊGÌ*ÉJǼÍ?Ç?Î=Ï=Ç?Ð�ÊIn Table 1 we show the expected g factors for the three isomeric states. The difference between the two values for 69mNi comes from the assumed “pure” configuration. The first value is obtained for a neutron p1/2 coupled to two neutrons on g9/2, while for the second one the coupling is between a neutron on the f5/2 orbital and two neutrons on g9/2.

In order to estimate the count rate for the different isotopes of interest we performed calculations using the LISE program. To obtain a spin-aligned ensemble of nuclei one has to select the secondary beam at ~ 2 % higher than the center of the momentum distribution. This brings the count rate to about 6 times lower, compared to the center of the momentum distribution at a momentum acceptance of ± 0.5%. This gives production rates for 70Ni, 69Ni and 67Ni, respectively, to 340 pps, 1100 pps and 5000 pps, if an average of 8 pnA primary beam intensity is assumed. Momentum slits of ± 0.5% were used for 70Ni and 69Ni and ± 0.25% for the 67Ni case. Additionally a factor of 1/8 was considered, which accounts for the well known overestimate of the LISE program, compared to the experimentally observed production rates, and for the transmission losses to the experimental vault [14].

g factors Isomer

t 1/2 Most intense Ñ - lines [keV]

Effective Empirical 67mNi 13.3 Ò s 313, 694 (-) 0.125 ± 0.006

69mNi 0.44 Ó s 148, 593, 1959 - 0.23/ - 0.22 - 0.19/ - 0.21

70mNi 0.23 Ô s 183, 448, 970, 1259 - 0.298 - 0.270 Õ�Ö�×�Ø Ù¼Ú�ÛIÜ�Ö�Ø Ý�ÞBØ ß à�Ù�á â=ã äBå æ ç�è�éëê!ç�ì�è*í�î+è�ï�ð è�ìñ:ò�ê�ï�ð ó�ô éõò�ó�ôëð ö�è¼ð ö�ô è�è¼æ é ó�÷�è�ô æ ï¼é ð ê�ð è�é øIù�ö�è¼è ò�ò�è�ï�ð æ ú�è¼ú�ê�å û�è�éëê�ô èï�ê�å ï�û�å ê�ð è�ìüû�é æ ç�ñüñNý�þ�ÿ�������� � � � �� ������������ ��� ����������� ���� !����������� ����� ��" ��#$�� �� %'&(��)�������� �*��%�" ��� � +,�*���� �������#-&*./����" 0��� !� %1" �������&�� 0�%��� ����2����� ���3./0��5476 8�9;:<: =?>A@�B2B�C�D�B�E�: F*B�G�> H�I I JLK�M�=�B�E�N�B�O;K�G3B�P/E�K�FRQ�B P/S�TVU�WXS

In order to estimate the necessary beam time we performed GEANT simulations using the realistic setup, as presented in Fig. 4. The spin alignment used in the simulations was equal to the one obtained in the 61mFe experiment. The results are shown in Fig. 5. They were obtained simulating 25 million implanted isomers, for each of the cases of 69Ni and 70Ni, and 100 million for 67Ni. The higher number of necessary implanted isomers for the latter case is due to its much longer half life (t1/2 ~ 13 µs). Additionally a case in which the values of the g factors are reduced by a factor of ~ 2 (similarly to 67mNi) has been simulated. It showed that with the presently mentioned statistics and a magnetic field of 0.5 T (a value achievable by the Y -NMR electromagnet) at least one and a half periods of oscillation can be observed for the 70Ni case.

Z�[ \�]�^�]�_*`Xa�b;ced�[ f*g�h i�j [ k�l�d�m/k�n?j o�p2q�i�d�p2krmesAtvu�w;x y/zv{|�};~<�����e�7� ���;� �Taking into account the GEANT simulations, the above mentioned count-rate estimates, and estimated isomeric ratios of 20%, 30% and 35%, respectively for 69mNi, 70mNi and 67mNi, we arrived to the following beam-time request. We need ���R�������<� to measure the g factor of �'�����,� , �����������<�

for �' �¡�¢,£ and ¤�¥�¦�§�¨�©<ª to perform a calibration using the known g factor of «'¬�­�®,¯ . Additionally °²±�³�´�µ<¶ of beam time are necessary for the initial tuning of our setup. This adds up to a total of ·�¸�¹»º�¼�½�¾<¿�ÀÂÁ<Ã�ÄÆÅV¼�Ç�ÅVÈVÃ�¾<É�Á<È!ÈVÊ�ÄÆÁ requested.

The necessary Ë�Ì<Í�ÎÐÏ�Ì<ÑÓÒÓÔ�Ì<Õ<Ö»×VÒ�ÎØÌ1ÒÓÙ�Ú�Û»Ü�Ý�Þ�Õ<Ù .

[1] G. Georgiev ß�à<á�â ã J. Phys. ä�å�æ , 2993 (2002) [2] R. Broda ç�èXé�ê ë ì Phys. Rev. Lett. í�î , 868 (1995) [3] T. Ishii ï�ð<ñ�ò ó ô�õ�ö'÷ùø�ó�ú�ï�û�ó�üùï�ð ð ó ô<ý�þ , 39 (2000) [4] H. Seifert ÿ������ � �������� ������������ , 25 (1994) [5] P.G. Reinhard et al., RIKEN Review ��� , 23 (2000) [6] O. Sorlin et al., Phys. Rev. Lett. ��� , 092501 (2002) [7] S. Leenhardt ������� � �� �!�"���#�$�%�&���'�(�!�"�)�� ��*,+.- , 1 (2002) [8] M. Hannawald et al., Phys. Rev. Lett. /�0 , 1391 (1999) [9] K.H. Langanke et al., Phys. Rev. C67, 044314 (2003) [10] R. Grzywacz 1�2�3�4 5 , Phys. Rev. Lett. 6�7 , 766 (1998) [11] L. Weissman 8�9�:�; < , Phys. Rev. =,>�? , 2004 (1999) [12] G. Goldring and M. Hass, @ A�BDC EF�G�H�I @ G�JLK�ANM,G�H�OQP�R STK�AVU�WX@ G�A�W�GLY (Ed: D. Allan Bromley, Plenum Press, New York, 1985), Vol. 3, p. 539. [13] I. Matea Z�[�\�] ^ , _ `Na�bdcfe�a�g h i�j�b�k[14] Tom Ginter, lfm�n o�p�q rts�u�v,v,w�x�n s�p�q n u�x�y