EXP # :
GANIL
PROPOSAL FOR EXPERIMENT
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Scheduling period :
June 2005 – May 2006
Dead-line for submission :
September 17th, 2004
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Title*:
The quadrupole moment
of the 9/2+ isomer in 61Fe
Is it a follow up experiment? yes
If yes, experiment number: E384
Spokespersons (if several, please use capital letters to indicate the name of the contact person):
Michael Hass (Weizmann Institute), Jean-Michel Daugas (Bruyeres le Chatel)
Address of the contact person:
Phone:
Fax:
E-mail:
Other Participants or Organisations:
G.Goldring, B.S.Nara Singh (Weizmann Institute);
G.Bélier, M.Girod, H.Goutte, V.Méot, O.Roig (CEA/DIF/DPTA/SPN Bruyères le Chatel);
P.Himpe, S.Mallion, G.Neyens, K.Turzo, N.Vermeulen, D.Yordanov (IKS, KULeuven);
G. Georgiev (CERN) ; I. Matea (CEN Bordeaux) ; F.de Oliveira-Santos, I. Stephan, C.Stodel, J.C Thomas (GANIL);
L.T.Baby (Florida State University); D.Balabanski (University of Camerino).
Abstract :
We propose to measure the magnitude and sign of the quadrupole moment of the neutron rich 61Fe (I=9/2+, t1/2=
245 ns) isomer. The recent determination of its g-factor confirmed the suggested spin/parity, with its configuration
dominated by the intruder g9/2 orbital. Calculations using HFB and the particle+rotor model suggest that this
isomer is deformed - most likely oblate - and coexisting with a prolate deformed ground state. Large Scale Shell
Model calculations confirm the oblate deformation, provided that several nucleon excitations are allowed. By
measuring the magnitude of the quadrupole moment, we will be able to check these predictions and provide
valuable input for these theoretical models.
Using an aligned ensemble of 61Fe isomers, obtained in a similar manner to a recent magnetic moment
determination of this isomer, the absolute value of Q can be measured. The subsequent determination of the sign
requires the use of the additional, unique feature of fragment beams: that it can be selected as a polarized beam.
This will be the first quadrupole moment measurement on an isomeric fragment beam.
Beam Line: LISE - D4
If Lise is requested, Wien Filter? No
Ion(s)
64Ni
Primary Beam(s)
Secondary Beam(s)
if Sissi is requested
Energy (A.MeV)
> 55
Intensity (nAe)
2000
Spiral Beam
Will you need Sissi ?
Lise production target ?
No
Yes
If yes, Sissi Target(s) and Thickness(es):
If yes, Lise Target(s) and Thickness(es): 9Be, 500 m
Requested number of beam UTs (1 UT=8h): 32 Time required for setting up the apparatus: 1 week
Time required for off beam calibration and dismount :
On what date would you be ready to run: June 2005
*
Excluded periods:
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2 days
Acquisition system: Ganil
Security, use of hazardous equipment : liquid N for detectors
(Radioactive target, liquid nitrogen, explosive gas etc.)
Comment :
1. Physics Motivation
The conventional shell structure changes drastically for nuclei with large neutron excess. The evolution of
shells, the vanishing of shell closures and the appearance of near magic numbers in neutron-rich nuclei have
been observed and intensively discussed. These phenomena are intimately related to the nuclear deformation
that can be determined in measurements of quadrupole moments. The quadrupole moment is sensitive to the
collective nature and is complementary to the determination of the magnetic moment that largely probes the
single-particle aspects of the corresponding wave function. Recently, measurements have been carried out
on nuclei with neutron numbers N~40 [1,2], addressing the role of the g9/2 orbital in this mass region. gfactors of isomers in 61Fe, 67Ni and 69Cu have been measured in previous TDPAD experiments at GANIL [3-5].
Recent experimental improvements have enhanced the experimental sensitivity with a factor of 10 compared
to the first such measurements. This opens the possibility to investigate more exotic cases and to measure
also nuclear quadrupole moments.
We propose to measure the Q-moment of an exited state in 61Fe, in which the g9/2 orbital manifests itself
as a low-lying, Ex = 861 keV (T1/2=245(5) ns) isomer with spin/parity 9/2+ (figure 1) [1,5,6]. It will be the first
isomeric Q-moment measurement ever done using a nuclear ensemble from fragmentation. Furthermore, a
unique feature of oriented fragment beams – namely the option to select a polarized ensemble – will allow to
measure the sign of the Q-moment as well.
Figure 1 : Left: The level scheme for the isomeric decay of 61Fe. Middle: Hartree-Fock-Bogoliubov meanfield calculations of surface energy as a function of deformation for various states using DIS Gogny force.
Right: Results of the large scale shell model calculations. The evolution of the first three states in 61Fe (top),
the quadrupole moment of the 9/2+ state (middle) and the magnetic moment of the 9/2+ state (bottom) with
increasing number of proton and neutron excitations.
Axial mean-field calculations have been performed using the effective nucleon-nucleon D1S Gogny force
[7,8]. Ground and excited states of the 61Fe nucleus are described within the Hartree-Fock-Bogoliubov (HFB)
formalism by expressing them as a one neutron quasi-particle blocked on a quasi-particle vacuum. The
ground state is found to be a K=3/2- state with a prolate charge deformation Q20=90 efm2, whereas an
excited K=9/2+ state is predicted with an excitation energy of 1.435 MeV and an oblate deformation Q20= 102 efm2, corresponding to  = -0.23 (see figure 1).
Large scale shell model calculations [9] (LSSM) were also carried out using the effective interaction
described in [10]. The 61Fe nucleus, with Z=26 protons and N=35 neutrons, was described as an inert 40Ca
core with a valence space consisting of the f7/2p3/2f5/2p1/2g9/2) and f7/2p3/2f5/2p1/2) orbitals. Eight neutrons
were blocked in the f7/2 orbital and up to six nucleons (tmax  6) were allowed to be excited to p3/2f5/2p1/2)
and g9/2). The energy of the first 9/2+ state depends strongly on the number of excited nucleons and only
converges to the experimental one when 6 particle-hole excitations are taken into account (figure 1). The
quadrupole moment shows a similar trend, going from Qs=-30.2 fm2 for one excited nucleon to Qs=-57.9 fm2
for 6 excited nucleons. Assuming 61mFe to be an axial deformed rotor with K=I=9/2, we obtain an oblate
charge deformation  2 = -0.24 for the converged value of the Q-moment. This is in excellent agreement with
the predictions of the HFB calculations. Note that the value of the magnetic moment remains practically
constant between tmax=2 and tmax=6, thus making it impossible to draw conclusions on the deformation from
the previous g-factor experiment.
It is instructive that the energy of the 9/2+ state converges to the experimental value when one increases
the model space in the LSSM calculations. This is a first indication that the used interaction correctly
describes this nucleus. The Q-moment determination will be a much more stringent test. It is important to
realise that the HFB calculations do not involve effective charges (e=e, e=0 was used), while in the LSSM
the standard effective charges for the protons and neutrons of 1.5e and 0.5e have been used. A
measurement of the Q-moment will help to define the proper effective charges for this enlarged shell model
space.
Although both the LSSM and HFB calculations predict an oblate shape for the 9/2 + isomer in 61Fe, there is
reason to assume that it may, in fact, have a prolate deformation. The moderate deformations that follow from
both calculations and the existence of the  orbital from the high j=9/2 shell near the Fermi level around
2=0.30, motivated us to study 61Fe in the framework of the particle plus rotor model [11]. Stephens et al. [12]
showed that for these conditions the movement of the valence nucleon can be coupled to the rotation of the
core (rotational alignment), leading to a rotational band starting from 9/2 + with a sequence of I  2 . This in
contrast to the normal deformation aligned band, which is constructed on  and characterized by a
sequence of I  1 . Calculations were performed for the two possibilities [11]. Both predict the 9/2 + state at
an energy close to the experimental one, so both the prolate and the oblate minimum in the HFB calculations
could give rise to a 9/2+ isomer. The calculated spectroscopic quadrupole moments for the oblate and prolate
state are both negative, Qs=-42 fm2 and Qs=-32 fm2, and therefore a measurement of the sign might not be
conclusive on the intrinsic shape (see below).
Measuring the quadrupole moment of the 9/2+ isomer in 61Fe will allow to prove unequivocally that this
isomer is indeed deformed, thus validating the HFB calculation. The obtained value can then be used as
input for the LSSM to determine the effective charges for the enhanced model space.
The subsequent measurement of its sign will allow to show the possibility of using the unique features of
spin-polarized beams to measure isomeric quadrupole moments with their sign.
2. Experimental method and set-up
We will use the Time Differential Perturbed Angular Distribution technique (TDPAD) on -heavy ion
correlated isomer decay transitions as described in Refs. [5,13] for the g-factor determination. The isomers
will be produced by the fragmentation of a 2 Ae, 55 MeV/amu 64Ni beam on a 9Be target and will be
selected by using the LISE spectrometer and an achromatic degrader of an appropriate thickness. In order
to increase the implantation rate and to avoid electron pick-up by the bare Fe ions, a thin (50 m thick)
plastic scintillator will be used to provide the time t = 0 signal for the subsequent isomer TDPAD
measurement. The use of bunch suppression will ensure the highest possible alignment during the
experiment [5], thus providing the basis for the TDPAD simulations presented below
In a quadrupole moment measurement, the interaction frequency between the nuclear quadrupole
moment and an electric field gradient, provided by the stopper crystal, is measured. A Cd single crystal with
an axially symmetric electric field gradient (EFG) will be used, because the implantation behaviour of Fe in
Cd is known from previous studies [14,15]. The EFG (VZZ) of Fe in Cd can be deduced from the earlier
measured quadrupole frequency of the 57Fe(3/2-,98 ns) isomer in Cd: Q(57Fe,3/2-) = +13.0(6) MHz [16].
Based on Mőssbauer studies and on recent microscopic calculations of the EFG of Fe in different FeX
systems [16], it has been shown that the earlier adopted reference Q-moment of the 57Fe isomer, used to
deduce the electric field gradient of Fe in different crystals, was wrong [17]. This was recently confirmed by a
combination of atomic and nuclear calculations [18], which suggest that the reference quadrupole moment for
the 57Fe isomer is Q(57Fe, 3/2-) = 15(2) efm 2. Using this value, we deduce the following electric field gradient:
Vzz(FeCd, 293 K) = 3.58(51) 1017 V/cm2.
TDPAD is a well-known method that has been used extensively in combination with the fusionevaporation reaction [14,15 and refs. therein]. Its application to fragmentation beams opens new
perspectives, but also poses some additional problems. With fragment beams, isomers in neutron rich nuclei
become available for moments studies. Another major advantage of fragment beams is the possibility to
select a spin polarized ensemble [19]. Polarized fragment beams have been successfully used at GANIL to
measure ground state g-factors of exotic nuclei via the  -NMR technique [20]. In the case of TDPAD, a
polarized beam is needed if one wants to measure the sign of the quadrupole moment [14]. In a
fragmentation reaction, a polarized beam is easily selected and thus provides a new and universal
way to measure the sign of Q-moments!
It is to be noted that the production rate for a polarized beam is considerably lower than for an aligned
beam. Furthermore, we do not exactly understand at this moment how to describe the density matrix of an
ensemble of isomers that is spin-polarized by the nuclear reaction, in which both alignment and polarization
might be present. Therefore, we suggest to commence by measuring the magnitude of the Q-moment using
an aligned beam (with known alignment from the g-factor experiment). At the second stage we repeat the
experiment with a polarized beam to obtain the sign and test if it is feasible to use polarized beams in the
future to directly determine simultaneously both absolute value and sign of quadrupole moments. To further
test the present method, we also propose to measure the well-known quadrupole frequency Q(54Fe, 10+) =
+45.3(9) MHz of the 10+ isomer (T1/2=364 ns) in 54Fe [14]. Furthermore, the ratio of the measured frequencies
yields the ratio of the respective Q-moments Q(61Fe,9/2+)/Q(54Fe, 10+) to a high accuracy (few %). As the
ratio for Q(54Fe,10+)/Q(57Fe, 3/2-) = 3.4(1) is known accurately from independent measurements in Zn and Cd
crystals [16], the relative quadrupole moments of the 54Fe, 57Fe and 61Fe isomers can be deduced very
accurately (few %). An accurate absolute determination will then depend on an improved adopted value for
the 57Fe reference, which is now given to 13% accuracy [18].
The difference between TDPAD in fusion-evaporation and fragmentation is the fact that the alignment
axis no longer coincides with the beam axis. Due to the precession of the spins in the magnetic field of the
separator, the alignment axis will be at an angle 
apparatus. Since this rotation depends on the g-factor, it is isomer dependent and considerably complicates
the positioning of the detectors and the c-axis of the crystal. To find the best experimental geometry we
developed a code that simulates the R(t) function for all possible orientations of the c-axis and positions of the
detectors, thus allowing to determine the optimal ones. We then investigated the dependence of the R(t)function on a possible misalignment of the detectors or the c-axis with respect to these optimal positions.
2.1 Magnitude of the Q-moment – TDPAD on a spin aligned ensemble
For the precision measurement of |Q|, a spin-aligned nuclear ensemble is selected and the optimal
configuration is found when the EFG symmetry axis ( ĉ ) is kept perpendicular to the detector plane and to the
alignment axis (fig. 2, left), with the -detectors placed at 90º with respect to each other and at 0º, +180º and
±90º with respect to the alignment axis. A deviation of up to 15º from this ideal position is allowed, in order not
to reduce the R(t) amplitude by more than 10% (fig. 4). By some lucky coincidence there is a 88º difference
between the alignment axis of 61Fe and 54Fe ((61Fe) = -114º and (54Fe) = -22º), so these two nuclei can be
measured with exactly the same experimental setup.
In figure 2, simulated R(t) functions for 61Fe (9/2+, T1/2=245 ns) and 54Fe (10+, T1/2=364 ns) isomeric
decays are shown. For the 61Fe isomer, the lowest and highest value as predicted by the LSSM calculations
has been used, since the HFB and the particle+rotor values lie also in this interval. Using the value of Vzz
derived above, this corresponds to the quadrupole frequencies Q=-26 MHz and Q=-50 MHz. The amplitude
is determined by the alignment angular distribution coefficient A22= 0.061, obtained from our recent g-factor
data [5]. The simulation of the R(t) function for the 54Fe(10+) isomer with Q(54Fe, 10+) = +45.3(9) MHz and
using the earlier observed A22=0.045, shows that the significant signal appears at 1400 ns only, which is
measurable as can be seen in the TDPAD spectra obtained from the previous experiment [5].
Figure 2 : Schematic drawing of the setup with an aligned beam (left). Simulated R(t) functions of
(middle) and 54Fe (right) for the Q-interaction of an aligned ensemble in a Cd single crystal.
61Fe
2.2 Sign of the Q-moment – TDPAD on a spin polarized ensemble
A polarized nuclear ensemble can be obtained by selecting the fragments at an angle with respect to the
primary beam. At GANIL, this is realized by a deviation of the primary beam, leading to a vertically oriented
polarization axis. Some alignment (as in the 0 degrees case above) may also remain in the selected
ensemble. In order to be sensitive only to the polarization component of the orientation, the crystal c-axis is
placed along the alignment axis (so different crystal orientation for each isomer is needed). The ideal detector
positions are now at ±45 and ±135 with respect to the c-axis (see fig. 3). The simulations are made for a
spin polarization of 5%, which is the amount we expect based on our previous experiences. For the opposite
sign of the Q-moment the R(t) function will show a phase shift of 180º. This will allow us to deduce the sign of
the Q-moment when the sign of the polarization is known. Several studies on spin-polarized fragment beams
have revealed a negative polarization for fragments selected in the right wing of the momentum distribution
[19].
Figure 3 : Schematic drawing of the setup with a polarized fragment beam (left). Simulated R(t) functions of
61Fe (middle) and 54Fe (right) for the Q-interaction of a polarized ensemble in a Cd single crystal. In the
simulations, only density matrix elements of the type (k,o) are considered. Elements with q≠0 may
complicate the picture.
The influence of placing the detectors away from their ideal positions given in figures 2 and 3, respectively
for an aligned and a polarized 61Fe beam, has been investigated in figure 4. Technical limitations or
considerations might make it favorable to do so. The amplitude of the R(t) function drops to 90% of its full
value if a pair of detectors deviates by 13º from the ideal position with respect to the alignment axis (or c-axis
in case of a polarized beam). Alternatively, a decrease (or increase) of the angle between two detectors by
18º also results in a reduction of the amplitude to 90%. This shows that a small misalignment of the detectors
with respect to their optimal positions has little influence on the R(t) amplitude.
Figure 4 : Sensitivity of the R(t) function on the misalignment of the detectors with respect to the alignment
axis for the aligned ensemble and with respect to the c-axis for the polarized ensemble (left). Sensitivity of
the R(t) function on the angle between the two detectors (right).
3. Beam time request
The experiment will be performed in the D4 room of LISE, using a 64Ni beam at 55 MeV/u and 2 Ae
(same as for E384). The production target, a 9Be foil of 500 m, is placed in the LISE target chamber. In
order to obtain a high degree of alignment or polarization, we have to select the fragments of interest in the
outer wing of the momentum distribution [5,17]. Under these conditions, the count rate for the aligned 61mFe
beam will be similar to that of Ref. [5]: N( 61Fe) ~ 10000/s with about 62% purity and a 50% isomeric ratio. For
the aligned ensemble we expect a Q-TDPAD amplitude of about 4%. Assuming the efficiency of each
detector somewhat less than 1 %, about 2·108 isomers have to be implanted, which corresponds to 56 hours
(=7 UT) of measurement for 61mFe. The calibration measurement on 54Fe(10+) will take another 5 UT. We also
need an additional 4 UT for the selection of the isomeric beams, making a total of 16 UT to measure the |Q|moments of 61mFe and 54mFe.
Similar arguments hold for the polarization case, where the estimated amplitude of about 2% will require a
total of 13 UT to measure the sign of the Q-moment of 61mFe. An additional 3 UT is needed for the selection
of the polarized beam. The beam time for the polarization (sign) case may be separated from the alignment
(|Q|) case, depending on practical scheduling considerations.
Total requested shifts: 32 UT.
References:
[1] R. Grzywacz et al., Phys. Rev. Lett. 81, 766 (1998).
[2] J. M. Daugas et al., Phys. Lett. B476, 213 (2000).
[3] G. Georgiev et al., Phys. Atom. Nuclei, 64, 1181 (2001).
[4] G. Georgiev et al., J. Physics G28, 2993 (2002).
[5] I. Matea et al., Phys. Rev. Lett. 2004 (in press)
[6] O. Sorlin et al., Nucl. Phys. A660, 3 (1999); Erratum Nucl. Phys. A669, 351 (2000).
[7] J. Dechargé and D. Gogny, Phys. Rev. C21, 1568 (1980).
[8] M. Girod, private communication and, M. Girod et al., Phys. Rev. C37, 2600 (1988).
[9] E. Caurier, shell model code ANTOINE, IRES, Strasbourg, 1989-2002
[10] O. Sorlin et al. , Phys. Rev. Lett. 88, 092501 (2002).
[11] I. Matea et al., Phys. Rev. C., in preparation.
[12] F. Stephens et al., Phys. Rev. Lett. 29, 438 (1972).
[13] G. Georgiev et al., AIP Conference Proceedings , Volume 701, Issue 1 (2004) 169-173
[14] M. Hass et al., Nucl. Phys. A414, 316 (1984).
[15] E. Dafni et al., Nucl. Phys. A443, 135 (1985).
[16] R. Vianden, Hyp. Int. 35, 1079 (1987).
[17] P. Blaha, private communication.
[18] G. Martinez-Pinedo et al., Phys. Rev. Lett. 87, 062701 (2001).
[19] D. Borremans et al., Phys. Rev. C 66, 054601 (2002).
[20] D. Borremans et al., Phys. Lett. B 537, 45 (2002), P. Himpe et al., Phys. Rev. Lett. 2004, in preparation