Nuclear Mass Measurements Map the Structure of Atomic Nuclei and Accreting Neutron Stars
Z. Meisel, S. George, S. Ahn, D. Bazin, B. A. Brown, J. Browne, J. F. Carpino, H. Chung, R. H. Cyburt, A. Estradé, M. Famiano, A. Gade, C. Langer, M. Matoš, W. Mittig, F. Montes, D. J. Morrissey, J. Pereira, H. Schatz, J. Schatz, M. Scott, D. Shapira, K. Smith, J. Stevens, W. Tan, O. Tarasov, S. Towers, K. Wimmer, J. R. Winkelbauer, J. Yurkon, R.G.T. Zegers
NNuclear Mass Measurements Map the Structure of Atomic Nucleiand Accreting Neutron Stars
Z. Meisel, ∗ S. George, S. Ahn, D. Bazin, B.A. Brown,
4, 5, 6
J. Browne,
4, 5, 6
J.F. Carpino, H. Chung, R.H. Cyburt,
4, 5
A. Estrad´e, M. Famiano, A. Gade,
4, 6
C. Langer, M. Matoˇs, W. Mittig,
4, 6
F. Montes,
4, 5
D.J. Morrissey,
4, 11
J. Pereira,
4, 5
H. Schatz,
4, 5, 6
J. Schatz, M. Scott,
4, 6
D. Shapira, K. Smith, J. Stevens,
4, 5, 6
W. Tan, O. Tarasov, S. Towers, K. Wimmer, J.R. Winkelbauer, J. Yurkon, and R.G.T. Zegers
4, 5, 6 Institute of Nuclear & Particle Physics, Department of Physics & Astronomy, Ohio University, Athens, Ohio 45701, USA Universit¨at Greifswald, Institut f¨ur Physik, Greifswald 17487, Germany Cyclotron Institute, Texas A&M University, College Station, Texas 77843, USA National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA Joint Institute for Nuclear Astrophysics – Center for the Evolution of the Elements,Michigan State University, East Lansing, Michigan 48824, USA Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA Department of Physics, Western Michigan University, Kalamazoo, Michigan 49008, USA Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA Department of Energy Technology, University of Applied Science Aachen, Campus J¨ulich, 52428 J¨ulich, Germany Physics Section, International Atomic Energy Agency, Vienna 1400, Austria Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA Department of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan (Dated: April 30, 2020)We present mass excesses (ME) of neutron-rich isotopes of Ar through Fe, obtained via TOF- Bρ mass spectrometry at the National Superconducting Cyclotron Laboratory. Our new resultshave significantly reduced systematic uncertainties relative to a prior analysis, enabling the firstdetermination of ME for , Ti, V, Cr, , Mn, and , Fe. Our results show the N = 34subshell weaken at Sc and vanish at Ti, along with the absence of an N = 40 subshell at Mn. Thisleads to a cooler accreted neutron star crust, highlighting the connection between the structure ofnuclei and neutron stars. The rest mass m is a basic property of an atomicnucleus, essential for calculating astrophysical processessuch as X-ray burst light curves and r -process nucleosyn-thesis, and key to mapping the evolution of nuclear struc-ture across the nuclear landscape [1–3]. While nuclearmasses nearly follow the whole-number rule, m ≈ Am u ,where A is the mass number and m u = 931 .
49 MeV isthe atomic mass unit, the (cid:46)
1% deviation from this re-lationship due to nuclear binding is notoriously difficultto predict. State-of-the-art mass models [e.g. 4–7] oftendisagree in their predictions of the atomic mass excess,ME(
Z, A ) = m − ( Z + N ) m u where Z is the proton num-ber and N is the neutron number, by more than oneMeV. Similar discrepancies are present when comparingpredictions to experimentally measured masses. As such,experiments mapping the evolution of the nuclear masssurface across the nuclear landscape are essential.For neutron-rich nuclides, mass measurements have re-vealed the emergence and disappearance of the magicnumbers that indicate enhanced nuclear binding [e.g 8–15]. For instance, N = 34 semi-magicity emerges forneutron-rich calcium isotopes [14], whereas there are sig-natures that the N = 40 harmonic oscillator subshell gapdisappears for neutron-rich manganese [16]. While theevolution of these subshells were mapped by spectroscopy experiments that often long-preceded the correspondingmass measurements [e.g. 17–24], nuclear masses providedthe first model-independent confirmation of this spectro-scopic evidence via fundamental ground state properties.These evolutions in nuclear structure are closely linkedto the thermal structure of accreting neutron stars. Nu-clei produced by surface burning processes are buriedby subsequent accretion, resulting in a number of nu-clear reactions in the neutron star crust that drive itfrom thermal equilibrium [25]. Electron-capture (EC)reactions near closed shells result in relatively large EC-heating due to the large change in the EC Q -value Q EC = ME( Z, A ) − ME( Z − , A ) [26]. EC in regionsof deformation between closed shells occur on isobarswith a small odd-even staggering in Q EC as well as low-lying excited states, which results in the EC- β − -decaycycling process known as urca cooling [27]. Therefore,whether EC heating or cooling occurs, and the strengthof the heat source or heat sink, strongly depend on nu-clear masses [28–30].To simultaneously map the evolution of the N = 34and N = 40 subshells and constrain the thermal struc-ture of accreting neutron stars, we performed mass mea-surements of neutron-rich isotopes of Ar through Fe( Z = 18 − a r X i v : . [ nu c l - e x ] A p r have been reported in Refs. [10, 29, 30]. The presentwork is a re-evaluation of the original data, incorporat-ing recently published high-precision Penning trap massdata [12, 13] as additional calibration nuclides, whichgreatly reduces the systematic uncertainty present in ourresults and greatly expands the number of nuclides forwhich masses are obtained. Our results extend the knownnuclear mass surface, provide model-independent confir-mation of the emergence of N = 34 and disappearanceof N = 40 semimagicity, and significantly update predic-tions for urca cooling in accreted neutron star crusts.Magnetic-rigidity corrected time-of-flight (TOF- Bρ )mass measurements were performed at the National Su-perconducting Cyclotron Laboratory. The measurementtechnique and measurements are described in detail inRefs. [10, 29–32] and are only briefly summarized here.A 140 MeV/nucleon beam of Se accelerated by thecoupled cyclotrons impinged on a Be target and the re-sulting fully-stripped (charge q = Z ) fragments weretransmitted through the A1900 fragment separator [33],momentum-analyzed at the target location of the S800spectrograph [34], and stopped in the focal plane of theS800 [35]. Particle identification was performed event-by-event using the TOF-∆ E method, where TOF wasprovided by fast-timing scintillators separated by a flightpath L path = 60 . E determined us-ing an ionization chamber. A relative measurement of Bρ , which is the momentum over q , was obtained via aposition measurement using a microchannel plate detec-tor located at the dispersive focus of the S800 [36, 37].Nominally, m = (TOF /L path )( qBρ/γ ), where γ is theLorentz factor. However, determining L path and Bρ tosufficient precision is not practicable. Instead, an em-pirical relationship between m/q and TOF is determinedfrom a fit to nuclides of known m which are simulta-neously measured alongside nuclides of interest. Thiswork improves on prior results [10, 29, 30] by includingseven additional calibration nuclides, bringing the totalto 27. High-precision ME for − Cr [13] and , Ti [12]substantially improve constraints on the m/q (TOF) re-lationship, whose ambiguity previously provided one ofthe dominant contributions to our ME uncertainties [30].Mass fits were performed as described in Ref. [30]. Sev-eral fit functions were explored, of the form mq ( τ ) = a + a τ + a z + a τ + a z + a zτ + f ( z, τ ) , where τ = TOF − (cid:104) TOF (cid:105) , z = Z − (cid:104) Z (cid:105) , and f ( z, τ )is a function of higher-order in z and/or τ . The addi-tion of the new Ti and Cr reference nuclides resolvedthe previously existing ambiguity in the Z -dependence,while the Cr masses additionally clarified that a higher-order TOF component was needed to adequately min-imize fit residuals, which are shown for the best-fit inFig. 1. The best-fit function has f ( z, τ ) = a z + a τ ,whereas a fit of slightly lower quality was obtained with f ( z, τ ) = a z + a τ . This set of acceptable functionswas determined by the following criterion. (1) The fitresiduals must lack systematic trends. (2) The fit resid-uals must be robust to the arbitrary removal of referencenuclides. (3) The difference between χ for a fit functionand the best-fit ∆ χ i = χ i − χ must be within threestandard deviations of the best-fit (∆ χ i (cid:46) A/Z - - - [ k e V ] li t e r a t u r e - M f i t M
44 45 46 4747 48 49 50 5149 50 51 52 53 5454 5559 60 61 62 6363 65 6664 66
Z=18Z=19Z=20 Z=22Z=24Z=25Z=26
FIG. 1. Residuals of the m/q (TOF) fit to calibration nuclides,where the isotope of an element is indicated by the numbernext to the data point. Red data are new calibration nuclidesin this re-evaluation. The gray band represents the averagesystematic mass uncertainty from the χ normalization.
28 30 32 34 36 38 40 42 44 N [ M e V ] S Cl Ar K Ca
Sc Ti V Cr MnFe Co
FIG. 2. S n for isotopes of Cl (left-most trend line) throughCo (right-most), where the black and gray open circles corre-spond to values using the 2016 AME [39] or higher-precisionME from the subsequent literature [12, 13, 40, 41], dashedlines are odd- Z , and solid lines are even- Z . Red filled circlesare from this work. The smaller number and closer similarity of the setof acceptable functions substantially reduce the fit-function uncertainty relative to the previous evalua-tion [30]. Additional uncertainty contributions comefrom the 9.1 keV/ q systematic uncertainty added to allnuclides to normalize the reduced χ to one for the best-fit and the uncertainty in a i due to TOF uncertainties inthe reference nuclides. See Ref. [30] for details.Our resultant ME are reported in Tabs. I and II withcomparisons to literature values and results from our pre-vious evaluation, where Fig. 2 shows the two neutron sep-aration energy S n ( Z, A ) = 2ME(0 ,
1) + ME(
Z, A − − ME(
Z, A ). All but one of our updated ME are within1 standard deviation σ of our previous ME and all arewithin 2 σ , while the majority of uncertainties have beenreduced by a factor of two. We report ME for , Ti, V, Cr, , Mn, and , Fe for the first time.The new trend in S n for V is largely due to , V,which are much less bound in our work compared tothe 2016 AME evaluated result, but in agreement withthe privately communicated results Ref. [39] refers to as that were included in that evaluation. The ab-normal behavior for Fe in S n shown in Fig. 2 is difficultto understand in terms of nuclear structure effects, sincea new single-particle orbital is not expected to be filled.Additionally, anomalous behavior of m/q (TOF) is an un-likely explanation, since the function is smooth in thatregion and a similar feature is not seen for nearby Z . Feis known to have an isomeric state at 387 keV [42], which,along with measurement uncertainties, may explain the ∼ S n from a smooth trend. Wesuspect Fe may also have a long-lived isomer based onthe presence of such states in odd- A isotopes of Fe due tointrusion from the νg / orbital [43]. The kink at N = 39for Cr agrees with the trend calculated using the LNPS’Hamiltonian [13, 30, 44], but the absolute S n are dis-crepant.ME for N = 36 isotopes of Sc, Ti, and V can be used todeduce the evolution of N = 34 in this region. Ref. [14]demonstrated the presence of N = 34 semi-magicity forCa, whereas spectroscopy has indicated this subshell clo-sure is absent for Ti and likely weakened for Sc, with thecaveat that E (2 +1 ) energies can provide ambiguous con-straints on shell gaps [45]. Our data reveal a continuousslope in S n for Ti following N = 34, while Sc trendsslightly more negative beyond this point. This indicatesthat a weak N = 34 subshell gap is present at Sc.Further insight is provided by the trend in D n ( Z, A ) =( − N +1 [ S n ( Z, A + 1) − S n ( Z, A )], which is related tothe empirical pairing gap [46]. D n is proportional to thenumber of angular momentum projection states (2 j + 1)participating in pairing, providing a signature of gaps insingle particle levels. Fig. 3(a) shows the trend in D n near N = 34 for isotopes of Ca through V. While thedip after N = 34 for the Sc isotopes might initially ap-pear to be the signature of a significant shell gap, shellmodel calculations suggest this is not the case. Calcu-lations using the GX1A Hamiltonian [47], whose resultsare shown in Fig. 3(b) to be in qualitative agreement
28 30 32 34 36 38 N [ M e V ] n D CaSc TiV (a)
28 30 32 34 36 38 N [ M e V ] n D (b) Sc ,Expt Sc,GX1A
36 38 40 42 44 N [ M e V ] n D CrMnFeCo (c)
FIG. 3. D n using our ME (filled circles) and ME from theliterature (open circles) (a) near N = 34 and (c) near N =40. A comparison to shell model calculations with the GX1AHamiltonian (filled-squares) is shown for Sc in (b). TABLE I. Atomic mass excesses (in keV) of nuclides determined in this work compared to the previous evaluation [10, 29, 30],the 2016 Atomic Mass Evaluation (AME) [39], and literature published after the 2016 AME. A * near the AME value indicatesthis is an extrapolation and not directly based on experimental data. The I following an isotope indicates a known or suspectedlong-lived ( >
100 ns) isomeric component. For instance, for Fe the known isomer at 387 keV excitation energy is responsiblefor the additional asymmetric error bar, while for Fe our results should be interpreted as an upper bound.Isotope This Work Previous Evaluation AME 2016 Literature Ar −
22 390 (260) −
22 280 (310) −
22 280 (310) −
22 330 (120) [14] Ar −
16 300 (1100) −
17 820 (1100) −
17 190* (400*) . . . Sc −
40 620 (230) −
40 300 (520) −
40 443 (82) −
40 525 (65) [15] Sc −
38 400 (210) −
38 170 (570) −
38 906 (94) −
38 910 (80) [15] Sc −
34 050 (240) −
33 750 (630) −
33 890 (273) −
34 485 (360) [15] Sc −
31 090 (220) −
30 520 (580) −
30 159 (454) . . . Sc I −
25 380 (260)( +0 − ) −
24 850 (590)( +0 − ) −
24 852 (587) . . . Sc −
20 180 (880) −
21 010 (1320) −
20 996 (1304) . . . Ti −
39 480 (240) . . . −
39 320 (121) −
39 810 (190) [15] Cr −
33 640 (300) −
33 480 (440) −
33 480 (440) . . .TABLE II. Table I continued, for cases without a PreviousEvaluation or Literature value.Isotope This Work AME 2016 Ti −
34 500 (240) −
33 916 (256) Ti −
30 890 (250) −
31 110* (200*) Ti −
25 220 (270) −
25 510* (200*) V −
44 650 (260) −
44 413 (80) V −
39 720 (230) −
40 402 (89) V −
37 040 (260) −
37 832 (162) V I −
32 810 (230)( +0 − ) −
33 242 (220) V −
30 380 (280) −
30 506 (894) V −
25 340 (420) −
25 476* (298*) Cr −
27 280 (780) −
28 220* (300*) Mn −
33 960 (330) −
33 460* (300*) Mn −
27 710 (1310) −
28 380* (400*) Fe I −
45 560 (320)( +0 − ) −
45 610 (270) Fe −
44 360 (320) −
43 487 (365) Fe I −
40 270 (400)( +0 − ? ) −
39 030* (400*) Fe −
37 710 (490) −
36 510* (400*) with experiment, indicate that the particularly low D n for Sc is due to the large splitting of levels created bythe residual interaction between the πf / and νf / or-bitals. In particular, the minimum in D n for Sc is due tothe low-lying J = 1 level created by this interaction. S n is not sensitive to this effect as it reflects the energeticsof neutron shells and not the strength of proton-neutronpairing [3, 16]. These results confirm previous indica-tions from spectroscopy of weak N = 34 magicity for Sc,while removing the ambiguity inherent to spectroscopicinterpretations of shell structure [18, 20, 45].Fig. 2 demonstrates a continuous slope in S n through N = 40 for Mn, strengthening the conclusions of Ref. [16]that the N = 40 subshell is absent for this element. Thisis bolstered by the trend in D n shown in Fig. 3(c). Ourdata are ambiguous regarding the N = 40 subshell atCr, where the mass of Cr is needed to confirm priorspectroscopic and coulomb-excitation evidence [e.g. 23,48, 49].The evolution in nuclear structure presented here isdirectly linked to the thermal structure of accreting neu-tron stars. The neutrino luminosity from urca cooling L ν ∝ X ( A )( f t ) − | Q EC | , where f t is the comparativehalf-life and X ( A ) is the mass fraction, and is thereforevery sensitive to changes in ME [50, 51]. This process op-erates in the accreted neutron star crust with consequen-tial L ν for odd- A nuclides with X ( A ) (cid:38) . f t (cid:46) (cid:46) | Q EC | (cid:46)
15 MeV [27, 52], where the upper limiton Q EC is due to competing EC reaction channels [53].Two EC parents predicted to produce some of the largest L ν , with potentially observable consequences [51, 52], are Sc and Mn. For Mn, f t will be uncertain by ordersof magnitude until measurements are enabled by next-generation rare isotope beam facilities, but estimatesfrom QRPA calculations [27] and using the Moszkowskinomographs [54] result in log( f t ) ≈
5, allowing signifi-cant L ν . Sc by contrast has more consistent predic-tions, with log( f t ) ≈ L ν urca cool-ing layer [52, 56]. Furthermore, a measurement of f t for this transition has recently taken place [57]. For both A = 55 and 65, X ( A ) > .
5% and are remarkably consis-tent for a wide variety of assumptions for nuclear burningon the accreting neutron star surface [58]. Therefore Q EC are the final piece of the nuclear physics puzzle for theseurca coolers.Using the newly determined ME( Sc), | Q EC ( Sc) | =12 .
44 (0 .
27) MeV, to be compared to the prior [14, 39]value 11.51 (0.48) MeV. Our reported ME( Cr) resultsin | Q EC ( Mn) | = 13 .
69 (0 .
78) MeV, to be compared tothe prior [16, 39] value 12.75 (0.30) MeV (though the lat-ter uncertainty relies on the AME extrapolation, whichassumes an essentially featureless nuclear mass surfaceand may be underestimated). These results increase L ν by 50% for EC on Sc with half the prior uncertainty andprovide the first experimental determination of L ν for ECon Mn. While in agreement with previous predictions,our central value for Q EC ( Mn) leads to 40% larger L ν .Therefore the accreted neutron star crust is cooler thanpreviously thought, with an improved precision on thedescription of the neutron star thermal structure.In conclusion, this work highlights the intriguing con-nection between evolution in nuclear structure and thethermal structure of accreting neutron stars. We findmodel-independent evidence for the onset of the N = 34subshell for Sc and the likely absence of N = 40 magicityfor Cr, each of which result in a larger mass differencefor transitioning from odd- Z to odd- N in EC. This is ul-timately connected to the strength of the interaction be-tween a nuclear core and an unpaired proton as opposedto an unpaired neutron [16, 59], and leads to increas-ing the phase-space available for the weak transitions in-volved in urca cooling, which in turn results in a coolerneutron star crust. 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