On the question about energy of 3.5 eV state of 229 Th S.L. Sakharov Petersburg Nuclear Physics Institute, Gatchina, Russia

 =  = The energy of the first isomeric state in 229 Th was determined to be  =3.5  1.0 eV, using the following combinations of level energies from the level scheme: The 229 Th level scheme Left side: the level scheme (8 excited states, 15 transitions) from ref. [1]. Right side: the levels introduced in the present work using the transition energies from ref. [1]. Energies are given in keV.ref. [1]. where  is the isomer energy and in square brackets the differences of transitions energies (not the energies themselves, as in the first two relationships) are taken.  = [ ]-[ ]  = [ ]-[76-74]

Placement of some transitions in 229 Th level scheme Energy of transition, Placement of transition, to 3.5 eV isomer or to the g.s. Reference, year of publication keV 1994 [1] Helmer 1999 [8] Firestone 2002 [9] Gulda 2003 [2] Barci 2005 [4] Helene 2006 [7] Ruchowska 2007 [5] Beck 29isomer g.s., isomer isomer g.s., isomer 71isomer g.s., isomer isomer g.s., isomer 146isomer g.s.isomer g.s., isomer g.s.

Lower part: dashed line is for the level scheme ( 8 excited states and 15 transitions), each point is for the same scheme but with 14 transitions, with each transition in turn being removed from the scheme. Upper part: dashed line is for the enlarged level scheme ( 14 excited states and 31 transitions), each point is for the same scheme but with 30 transitions, with each transition in turn being removed from the scheme. The energy of the isomeric transition  depending on the energy of the transition excluded from the 229 Th level scheme from ref.[1].ref.[1]. Fig.2.

The close level spacing between the two bandheads raises the question of determining the correct intensities of the transitions between the lower states. The low energy multiplets.Fig. 6

Fig 1. Level scheme and  -ray transitions of 229 Th from ref.[4]. (Continuous arrows) Undisputed  - ray transitions; (dashed and dotted lines) not well-established  -ray transitions; (spins and parity) left side, Ref. [2] Barci; right side, Ref. [9] Guldaref.[4]. Ref. [2] Barci; Ref. [9] Gulda Th 139

Table I. Different hypotheses about some  – ray transitions in 229 ThDifferent hypotheses  -ray energy Initial level Final level (keV) (keV) Ref.[Beck]BeckRef.[Barci]Barci Ref.[ Helene] Helene Ref.[ Gulda] Gulda 29 92% 8% 75% G.S.25% 49% 51% 3.5 eV7.6(5)eV9.3 (6)eV14.3 (10)eV 71 60% G.S.40% 59% 41% 146 G.S % G.S. 12%

Fig. 1. The two rotational bands are displaced relative to each other for clarity, and labeled by the Nilsson asymptotic quantum numbers. The gamma rays of the [631] band are distinguished by green coloring. Partial level scheme ref. [5] Partial level scheme ref. [5] of 229 Th with E  in keV.

Data illustrated for the 29 keV doublet (  E 29 ) is the sum of 11 data sets and 25 pixels (a), and data illustrated for the 42 keV doublet (  E 42 ) represents the sum of 11 data sets only for pixel 0 (b). Black lines represent the data; red lines represent the least-square fitting results. Full-energy peaks are labeled by J   of the corresponding 229 Th transition. XRS spectra in 29 and 42 keV energy regions.XRS spectra in 29 and 42 keV energy regions. ref.[5] Fig. 2.

In ref.[5] the eV, eV, eV and eV transitions were taken with the resolution of eV. The energy of the first isomeric state E( 229m Th) was determined from relationship E( 229m Th) =  E 29   E 42 =  0.50 eV   0.22 eV = 7.0  0.5 eV, where  E 29 = (29.39  29.19) keV =  0.50 eV, which means the error of the keV transition is 0.50 eV or larger (intensity of the keV transition  intensity of the keV transition  40). However judging from fig. 2a of ref.[5] the intensity of the keV transition within 26 eV FWHM is about 300 counts. So the minimal achievable error is 26  = 1.5 eV. Even if one takes the intensity of the keV transition  0.5 per day per pixel, its total intensity (not within FWHM) is 2  11 days  25 pixels = 550. Within FWHM the intensity is about 400, so the resulting error is 26  =1.3 eV. So the accuracy of the energy error of the keV transition and hence of  E 29 is overestimated, which possibly result in poor fit (3  ) of the keV transition in the level scheme of Helmer ref.[1]. The value of 7.0  0.5 eV was corrected by branching b = 1  13 from the keV level to the g.s., which gives 7.6  0.5 eV. However branching 25% from [2] results in the value of 9.3 eV. Energy calibration in the range keV was done using a 4th order polynomial with zero-energy offset.ref.[5] ref.[1].

Conclusions Therefore in reality the energy of the 3.5 eV state lies in the range 0  15 eV and it is not clear whether this state does exist. One may propose two ways to determine its energy: 1.The direct measurement of the energy of the transition from the 3.5 eV state. However, the attempts to find such a transition failed Richardson [10], S.B.Utter et al [11]. The task is very difficult because the possible range of the transition energies is very wide,Richardson [10], S.B.Utter et al [11]. 2.The direct measurement of the energies of the strongest 42 and/or 97 keV transitions to calculate the 3.5 eV state energy. A double crystal spectrometer similar to that from Gavrikov [12] with the resolution of the order of 1 eV is very suitable for this aim. For the source of 100 cm2 area containing 20 g of 233U one can expect to register 3  /h for the 97 keV transition and 14  /h for the 42 keV transition (assuming 100 % effectiveness of registration and a solid angle of 10-9).Gavrikov [12]

References 1.R.G. Helmer and C.W. Reich, Phys. Rev. C49 (4), 1845 (1994). 2.V. Barci et al., Phys. Rev. C68, (2003). 3.Z.O. Guimaraes-Filho, O. Helene and P.R. Pascholati, Contributions to Conference on Nuclear Physics, Santa Fe, 2005, p.257; 4.Z.O. Guimaraes-Filho and O. Helene, Phys. Rev. C71, (2005). 5.B.R. Beck, J.A. Becker, Beiersdorfer et al., Phys. Rev. Lett. 98, (2007) 6.J. Tuli. 7.E. Ruchowska et al., Phys. Rev. C73, (2006) 8.R.B. Firestone, S.Y.F. Chu, and C.M. Baglin, Table of Isotopes CD-ROM, 8th ed. (Wiley- Interscience, New York, 1999) 9.K. Gulda et al., W. Kurcewicz, A.J. Aas et al., Nucl. Phys. A703, 45, (2002). 10.D.S.Richardson et al., Phys. Rev. Lett. V.80, 3206 (1998). 11.S.B.Utter et al., Phys. Rev. Lett. V.82, 505, (1999) 12.Yu.A. Gavrikov et al., Preprint NP , Gatchina, 2000, p.42.

A portion of the low-energy level scheme of 229 Th showing the  rays that are used in this determination of the energy  of the first excited level.  =  =  =  = The energy, , of the first excited level is given by each of the four combinations of  –ray energies:

An excited state of 229 Th at 3.5 eV Table VII The energy, , of the first excited level a The energies for E  (25) and E  (29) are from Table V.Table V b The energies for E  (25) and E  (29) are derived in the text from the computed and differences for the 29 line and from the measured (Table III) difference for 25 line.(Table III)

Comparison of (d, t) strengths for rotational band members in 229 Th and 231 Th. Table 1. a This upper limit for the strength is obtained assuming the full cross section of the unresolved doublet is for this level. b Upper limit only. Peak is obscured by a larger one for a nearby level.

Cross section (μb / sr) Angle (deg) The solid curves are DWBA calculations for the l values appropriate for the states indicated, adjusted in the vertical direction to give the best visual fit to the data points. Angular distribution for (d, t) cross section of some 229 Th levels. Fig. 2