Trapped nobeliumions yield first direct measurements of transuranic masses

To first approximation, the mass of a nucleus is the sum of its constituent proton and neutron masses. But the roughly 1% correction for nuclear binding energy embodies important information about the configuration of the particular nucleus. Binding energies are especially interesting, and correspondingly hard to measure, in two cases: short-lived isotopes with unusually large or small neutron numbers N for their proton numbers Z, and the transuranic nuclei (Z > 92) approaching the so-called island of stability expected to be found somewhere near Z = 120 and N = 184. (See figure 1.)

Nowadays the best measurements of nuclear masses are done in Penning traps — small, cylindrically symmetric cavities in which charged particles can be kept away from the walls by static electric and magnetic fields and stored for long periods (see Physics Today, May 1985, page 17 ). Beyond its custodial function, the trap’s uniform axial magnetic field can reveal the mass of stored particles by the cyclotron frequency with which they orbit the axis. By such means, the masses of stable nuclei have been measured with precisions approaching a part in 10¹¹.

For short-lived nuclei, precision is limited by the time available for determining the cyclotron frequency. Still, Penning traps have yielded the masses of isotopes with half-lives as short as 10 milliseconds. But until now, there has been no measurement of the mass of any transuranic nucleus by Penning trap or any other “direct” means. Nuclear physicists have had to rely on measuring the kinetic energies of α particles emitted in α-decay chains extending down to cisuranic (Z ≤ 92) isotopes of well-measured mass. In favorable cases, such indirect mass determinations can yield binding-energy uncertainties smaller than 10 keV, more than adequate for comparison with current theoretical predictions. (The nucleon mass is about 1 GeV, and binding energies per nucleon are of order 10 MeV.) But some chains involve α decays to excited intermediate states that confound the energy bookkeeping. And others, especially decay chains starting with the heaviest known transuranics (up to Z = 118), terminate in fission before reaching terra cognita.

Now, however, a team at the GSI Helmholtz Center for Heavy Ion Research in Darmstadt, Germany, has reported the first ever direct mass measurement for transuranic nuclear species. ¹ Led by Michael Block, the team has measured the masses of three nobelium (Z = 102) isotopes in a Penning trap. The half-lives of the three isotopes, ²⁵²No, ²⁵³No, and ²⁵⁴No, range from two minutes down to two seconds. “That wasn’t the principal problem,” says Block. “The real challenge was the painfully slow rates at which such nuclei are produced in the lab by fusion reactions.”

Making and catching nobelium

The lightest transuranics can be made in high-flux reactors by neutron capture and subsequent β decay. Beyond fermium (Z = 100) however, experimenters have to smash accelerated ion beams into targets and tease out the desired fusion product. To create the several No isotopes, Block and company directed intense 220-MeV beams of calcium-48 ions at lead target foils of isotopically almost pure ²⁰⁶ Pb, ²⁰⁷ Pb, or ²⁰⁸ Pb, depending on which No isotope they were after. The desired reaction yields a fusion of beam and target nuclei minus two liberated neutrons.

Just downstream of the target, a 10-meter-long array of static magnetic and electric fields served as a velocity filter that transmitted the meager yield of emerging No candidates while diverting the torrent of much faster surviving beam ions and debris. With a beam flux of 10¹³ Ca ions per second hitting the ²⁰⁶ Pb target, less than one ²⁵²No ion per second passed through the velocity filter. For the other two No isotopes, the production rates were only slightly higher.

Emerging from the velocity filter with kinetic energies of about 40 MeV and large charges, the No ions were next injected into a helium gas cell to be thermalized to room temperature and reduced mostly to the +2 charge state. They then entered an ion guide in which RF quadrupole fields accumulated and bunched them for synchronous insertion into the first of two Penning traps in an ongoing sequence of half-second measurement cycles.

Like similar facilities worldwide, the GSI chain of heavy-ion accelerator, fusion target, velocity filter, and Penning traps has been used for some time to measure the masses of relatively rare cisuranic isotopes. In that context, it’s become habitual to speak of plural “ions” entering the Penning traps per cycle. But in this first foray beyond uranium, the production rates are so low that a given cycle rarely captures more than one ion. Often it captures none.

Tandem Penning traps

A charged particle in a Penning trap is confined in the trap’s axial direction by a weak electric quadrupole field. Radial confinement is accomplished by the strong axial magnetic field B, which keeps ions of mass m and charge q essentially in cyclotron orbits whose frequency

$${\nu }_{\text{c}}=qB/2\pi m$$

is independent of an ion’s energy—so long as it’s nonrelativistic. In the GSI experiment, the trapped ion’s ν _C was determined by resonant effects between ν _C and the adjustable frequency ν _RF of RF pulses imposed on the cavity.

The two sequential Penning traps in the GSI measurement chain sat together in the uniform 7-tesla field of a superconducting solenoid magnet. Any particle coming from the ion guide was first vetted by the so-called purification trap, which kept interlopers from the second, precision trap by passing on only particles whose ν _C resonated with an RF pulse whose frequency spread was just broad enough to encompass any doubly charged ion within 5 MeV of the desired isotope’s mass.

Any ion that made it to the precision trap was then subjected to a narrowband RF excitation pulse before leaving the trap and having its velocity gain measured. The trapped ion experienced resonant acceleration only if the imposed ν _RF was very close to its ν _C. Figure 2 shows the result of one four-hour cyclotron-resonance measurement for ²⁵³No. As the ν _RF passes through ν _C, the ion’s flight time to a downstream detector manifests the resonant excitation.

For each of the three No isotopes, Block and company carried out at least three such extended runs. To translate the measured cyclotron frequencies into precise masses, one has to know B with comparable precision or calibrate it with other ions of much better-known mass. Because the magnetic fields of superconductors inevitably suffer gradual decay by what’s called flux creep, the GSI team recalibrated the field every few hours with singly charged cesium-133 ions.

Comparing results

Figure 3 compares the No atomic masses thus obtained (after correction for the two missing electrons) with those given in the international Atomic Mass Evaluation (AME) consortium’s most recent (2003) compilation. All three GSI measurements are consistent with the AME masses, which were determined from α-decay chains. The most striking improvement is GSI’s eightfold reduction of the 100-keV uncertainty on the mass of ²⁵³No. The earlier uncertainty was so large because ²⁵³No’s α-decay chain involves excited states in fermium-249 and californium-245 whose energies and orderings were unclear. Such troublesome excited states are common in the α decays of “odd-even” nuclei, with neutron and proton numbers of opposite parity.

The other two isotopes, being even-even nuclei, don’t have that problem. So the uncertainties on their old AME masses were no worse than those of the new Penning-trap measurements. In fact, for ²⁵²No, which had the slowest production rate in the GSI experiment, the 30-keV uncertainty on the new mass is more than twice the AME uncertainty. “Nonetheless,” says Block, “the direct weighing of ²⁵²No against ¹³³Cs already adds reliability to a mass previously known only indirectly, from α-particle measurements that might involve significant unknown systematic errors.”

The GSI experiment was a proof-of-principle demonstration. All three No isotopes had fusion-production rates at least 10 times slower than that of any nuclide previously weighed in a Penning trap. The team hopes soon to reduce uncertainties significantly by raising the overall efficiency, now only about 3%, with which the desired nuclide created in the target makes it all the way through the measurement sequence. An important step will be enlarging and cryogenically cooling the helium gas cell.

The pairing bonus

To get the nuclear mass from the mass of a neutral atom, one has to consider not only the electron’s mass (0.51 MeV) but also its binding energy. In the absence of experimental data, the total electromagnetic binding energy of nobelium’s 102 electrons has to be estimated theoretically. But the error on that estimate is presumed to be negligible in the context of the Penning-trap measurements.

The nuclear binding energies, per nucleon, of all three No isotopes are near 7 MeV. With the masses of three adjacent isotopes in hand, one gets their neutron pairing energy Δ_n, an important quantity for discriminating between nuclear models. Defined as the difference between the mass of the middle nuclide and the mean of the two that flank it, Δ_n measures the binding-energy bonus gained by the pairing of outer-shell neutrons. For ²⁵²No-²⁵⁴No, the GSI experiment yields Δ_n = +565 ± 21 keV. The sign is positive, as one would expect when the middle isotope has the unpaired neutron.

For the superheavy nuclei approaching Z = 118, half-lives get ever shorter and production rates ever slower, eventually precluding mass measurement in Penning traps. But the direct measurement of masses for No and neighbors like rutherfordium (Z = 104) and dubnium (Z = 105) will provide terminal anchor points for α-decay chains originating as far up as Z = 116. And the demonstration that ions as rare as the GSI nobelium isotopes can be thermalized and trapped should make such exotic species accessible to laser and nuclear spectroscopy.