High-precision Mass Measurements Research Articles

Masses of transuranium nuclides measured with the PI-ICR technique at TRIGA-Trap

We have revisited the region of the actinides in the vicinity of the neutron number N=152 and conducted high-precision mass measurements using the newly implemented Phase-Imaging Ion-Cyclotron-Resonance (PI-ICR) technique. The masses of 244\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{244}$$\\end{document}Pu and 249\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{249}$$\\end{document}Cf were found to deviate by 5.4 and 2.9 combined sigmas, respectively, from our previous results published in 2014. This indicates the presence of systematic errors in the earlier measurements. Consequently, we decided to remeasure all the nuclides from our 2014 study, along with 248\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{248}$$\\end{document}Cm, to ensure accuracy and reliability. With our greatly improved apparatus, we have measured the masses of 244\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{244}$$\\end{document}Pu, 241\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{241}$$\\end{document}Am, 243\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{243}$$\\end{document}Am, 248\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{248}$$\\end{document}Cm, and 249\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{249}$$\\end{document}Cf, using 208\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{208}$$\\end{document}Pb and 238\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{238}$$\\end{document}U as mass references. The masses of these reference ions were recently determined with ultra-high precision at Pentatrap. Our results were implemented in the latest Atomic Mass Evaluation (AME), showing good consistency. The region related to the masses measured in this study, especially for isotopes near the N=152 deformed shell gap, is discussed in terms of two-neutron separation energies, first excited 2+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^+$$\\end{document} energy levels and their differentials, as well as δVpn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta V_{pn}$$\\end{document} values, the average proton-neutron interaction of the most loosely bound two nucleons.

High-Precision Mass Measurements of Neutron Deficient Silver Isotopes Probe the Robustness of the N=50 Shell Closure.

High-precision mass measurements of exotic ^{95-97}Ag isotopes close to the N=Z line have been conducted with the JYFLTRAP double Penning trap mass spectrometer, with the silver ions produced using the recently commissioned inductively heated hot cavity catcher laser ion source at the Ion Guide Isotope Separator On-Line facility. The atomic mass of ^{95}Ag was directly determined for the first time. In addition, the atomic masses of β-decaying 2^{+} and 8^{+} states in ^{96}Ag have been identified and measured for the first time, and the precision of the ^{97}Ag mass has been improved. The newly measured masses, with a precision of ≈1 keV/c^{2}, have been used to investigate the N=50 neutron shell closure, confirming it to be robust. Empirical shell-gap and pairing energies determined with the new ground-state mass data are compared with the state-of-the-art abinitio calculations with various chiral effective field theory Hamiltonians. The precise determination of the excitation energy of the ^{96m}Ag isomer in particular serves as a benchmark for abinitio predictions of nuclear properties beyond the ground state, specifically for odd-odd nuclei situated in proximity to the proton dripline below ^{100}Sn. In addition, density functional theory calculations and configuration-interaction shell-model calculations are compared with the experimental results. All theoretical approaches face challenges to reproduce the trend of nuclear ground-state properties in the silver isotopic chain across the N=50 neutron shell and toward the proton dripline.

Early Results from the HUMDRUM Survey: A Small, Earth-mass Planet Orbits TOI-1450A

M-dwarf stars provide us with an ideal opportunity to study nearby small planets. The HUnting for M Dwarf Rocky planets Using MAROON-X (HUMDRUM) survey uses the MAROON-X spectrograph, which is ideally suited to studying these stars, to measure precise masses of a volume-limited (<30 pc) sample of transiting M-dwarf planets. TOI-1450 is a nearby (22.5 pc) binary system containing a M3 dwarf with a roughly 3000 K companion. Its primary star, TOI-1450A, was identified by the Transiting Exoplanet Survey Satellite (TESS) to have a 2.04 days transit signal, and is included in the HUMDRUM sample. In this paper, we present MAROON-X radial velocities (RVs) which confirm the planetary nature of this signal and measure its mass at nearly 10% precision. The 2.04 days planet, TOI-1450A b, has R b = 1.13 ± 0.04 R ⊕ and M b = 1.26 ± 0.13 M ⊕. It is the second-lowest-mass transiting planet with a high-precision RV mass measurement. With this mass and radius, the planet’s mean density is compatible with an Earth-like composition. Given its short orbital period and slightly sub-Earth density, it may be amenable to JWST follow-up to test whether the planet has retained an atmosphere despite extreme heating from the nearby star. We also discover a nontransiting planet in the system with a period of 5.07 days and a Msinic=1.53±0.18M⊕ . We also find a 2.01 days signal present in the systems’s TESS photometry that likely corresponds to the rotation period of TOI-1450A’s binary companion, TOI-1450B. TOI-1450A, meanwhile, appears to have a rotation period of approximately 40 days, which is in line with our expectations for a mid-M dwarf.

Fleeting but Not Forgotten: The Imprint of Escaping Hydrogen Atmospheres on Super-Earth Interiors

Small, close-in exoplanets are divided into two subpopulations: super-Earths and sub-Neptunes. Most super-Earths are thought to have lost their primordially accreted hydrogen-dominated atmospheres via thermally driven winds. We consider the global chemical equilibrium of super-Earths and the lasting impacts of their fleeting hydrogen atmospheres. We find that hydrogen is efficiently sequestered into the interior, oxidizing iron and endogenously producing ∼0.5%–1.0% water by mass. As the atmospheres of super-Earths are continuously sculpted by mass loss and chemical equilibration, they remain hydrogen-dominated by mole (number) fraction but become steam-dominated by mass, which may be observable with JWST for planets transitioning across the radius valley. One of the main effects of efficient sequestration of hydrogen into the interior is to produce an underdense bulk interior compared to that of Earth. We predict bulk densities of super-Earths to be ∼5.0 g cm−3 for a 1M ⊕ planet, which is consistent with high-precision mass measurements and also population-level inference analyses from atmospheric escape models.

Long-sought isomer turns out to be the ground state of 76Cu

Isomers close to the doubly magic nucleus 78Ni (Z=28, N=50) provide essential information on the shell evolution and shape coexistence far from stability. The existence of a long-lived isomeric state in 76Cu has been debated for a long time. We have performed high-precision mass measurements of 76Cu with the JYFLTRAP double Penning trap mass spectrometer at the Ion Guide Isotope Separator On-Line facility and confirm the existence of such an isomeric state with an excitation energy Ex=64.8(25) keV. Based on the ratio of detected ground- and isomeric-state ions as a function of time, we show that the isomer is the shorter-living state previously considered as the ground state of 76Cu. The result can potentially change the conclusions made in previous works related to the spin-parity and charge radius of the 76Cu ground state. Additionally, the new 76Cu(n,γ) reaction Q-value has an impact on the astrophysical rapid neutron-capture process.

Fast adiabatic transport of single laser-cooled 9Be+ ions in a cryogenic Penning trap stack

High precision mass and g-factor measurements in Penning traps have enabled groundbreaking tests of fundamental physics. The most advanced setups use multi-trap methods, which employ transport of particles between specialized trap zones. Present developments focused on the implementation of sympathetic laser cooling will enable significantly shorter duty cycles and better accuracies in many of these scenarios. To take full advantage of these increased capabilities, we implement fast adiabatic transport concepts developed in the context of trapped-ion quantum information processing in a cryogenic Penning trap system. We show adiabatic transport of a single 9Be+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^9\ extrm{Be}^+$$\\end{document} ion initially cooled to 2 mK over a 2.2-cm distance within 15 ms and with less than 10 mK energy gain at a peak velocity of 3 m/s. These results represent an important step towards the implementation of quantum logic spectroscopy in the (anti-)proton system. Applying these developments to other multi-trap systems has the potential to considerably increase the data-sampling rate in these experiments.

Progress in High-Precision Mass Measurements of Light Ions

Significant advances in Penning trap measurements of atomic masses and mass ratios of the proton, deuteron, triton, helion, and alpha-particle have occurred in the last five years. These include a measurement of the mass of the deuteron against 12C with 8.5 × 10−12 fractional uncertainty; resolution of vibrational levels of H2+ as mass and the application of a simultaneous measurement technique to the H2+/D+ cyclotron frequency ratio, yielding a deuteron/proton mass ratio at 5 × 10−12; new measurements of HD+/3He+, HD+/T+, and T+/3He+ leading to a tritium beta-decay Q-value with an uncertainty of 22 meV, and atomic masses of the helion and triton at 13 × 10−12; and a new measurement of the mass of the alpha-particle against 12C at 12 × 10−12. Some of these results are in strong disagreement with previous values in the literature. Their impact in determining a precise proton/electron mass ratio and electron atomic mass from spectroscopy of the HD+ molecular ion is also discussed.

High-precision Penning-trap mass measurements of Cd and In isotopes at JYFLTRAP remove the fluctuations in the two-neutron separation energies

High-precision Penning-trap mass measurements of Cd and In isotopes at JYFLTRAP remove the fluctuations in the two-neutron separation energies

In Situ Tritium Decontamination of the KATRIN Rear Wall Using an Ultraviolet/Ozone Treatment

The KArlsruhe TRItium Neutrino (KATRIN) collaboration aims to determine the neutrino mass with a sensitivity of 0.2 eV/c2 (90% confidence level). This will be achieved by probing the end-point region of the β-electron spectrum of gaseous tritium with an electrostatic spectrometer. A gold-coated stainless steel disk defines the reference potential for high-precision neutrino mass measurement, and it terminates the β-electron flux as the physical boundary of the tritium source. This so-called rear wall is exposed to tritium, which leads to adsorption and absorption. This in turn leads to systematic uncertainties for the neutrino mass measurements that need to be understood and mitigated. In maintenance phases, during which the gaseous tritium source was emptied (<10−5 of nominal gas density), the activity that accumulated on the rear wall during normal operation was monitored using beta-induced X-ray spectrometry (BIXS) and direct observation of emitted β electrons with a silicon detector. Dependency of the observed activity increase on the integral tritium throughput was investigated and found to converge from limited exponential growth to continuous linear growth. This paper gives an overview of the results that were obtained using several methods of in situ decontamination of the rear wall while continuously monitoring the activity. The decontamination methods included heating during continuous evacuation; flushing the system with nitrogen, deuterium, or air with residual humidity at different pressures; and illumination of the rear wall with ultraviolet (UV) light. These well-known methods led to only a small ( ≈ 15%) decrease in the observed activity. However, a decrease of the surface activity by three orders of magnitude in less than 1 week was achieved by combination of different methods using UV light, a heated surface, and a low (5 to 100 mbar) pressure of air inside the chamber, leading to the production of highly reactive ozone. This proved to be by far the most efficient method, drastically reducing the contribution of the rear wall surface activity to the β spectrum of the gaseous source.

Toward neutrino mass from cosmology without optical depth information

With low-redshift probes reaching unprecedented precision, uncertainty of the cosmic microwave background (CMB) optical depth is expected to be the limiting factor for future cosmological neutrino mass constraints. In this paper, we discuss to what extent combinations of CMB lensing and galaxy survey measurements at low redshifts $z\ensuremath{\sim}0.5--5$ will be able to make competitive neutrino mass measurements without relying on any optical depth constraints. We find that the combination of LSST galaxies and CMB-S4 lensing should be able to achieve constraints on the neutrino mass sum of 25 meV without optical depth information, an independent measurement that is competitive with or slightly better than the constraint of 30 meV possible with CMB-S4 and present-day optical depth measurements. These constraints originate in both structure growth probed by cross-correlation tomography over a wide redshift range as well as, most importantly, the shape of the galaxy power spectrum measured over a large volume. We caution that possible complications such as higher-order biasing and systematic errors in the analysis of high-redshift galaxy clustering are only briefly discussed and may be non-negligible. Nevertheless, our results show that new kinds of high-precision neutrino mass measurements at and beyond the present-day optical depth limit may be possible.

Decay-correlated mass measurement technique via multi-reflection time-of-flight mass spectrograph with the [formula omitted]-TOF detector

The development of a technique to correlate ion mass with subsequent decay measurements using a multi-reflection time-of-flight mass spectrograph and the α/β-TOF detector has opened a new frontier, not only for high-precision mass measurements, but also for nuclear spectroscopy research. Herein we provide an overview of the decay-correlated mass measurement technique, describe the noise suppression capability, and discuss its use in high-precision mass measurements of superheavy nuclides.

Improved high-precision mass measurements of mid-shell neon isotopes

New mass values measured with the TITAN MR-TOF-MS are reported for the short-lived isotopes 24−26Ne, produced at TRIUMF's ISAC facility using a uranium carbide target and cold FEBIAD ion source. A least-squares adjustment within the framework of the Atomic Mass Evaluation was performed and the improved precision of the new mass values is highlighted. The improved mass accuracy in this N=14 mid-shell region can also point to the refinement in values of the charge radii. By reducing the mass uncertainty of isotopes, their contribution of the mass shift uncertainty in laser spectroscopy can be negated. The work is part of developments for reaching the N=20 Island of Inversion, where high molecular contamination hinders mass measurements of the neon isotopes.

First application of the phase-imaging ion-cyclotron resonance technique at TRIGA-Trap

The phase-imaging ion cyclotron resonance technique (PI-ICR) has been implemented at TRIGA-Trap together with a newly built five-pole cylindrical trap. In PI-ICR the total phase of trapped ions is measured by projecting the ion motion onto a position-sensitive delay-line micro-channel plate detector. The systematic uncertainties have been investigated and first mass measurements on stable Pb isotopes have been performed with PI-ICR. The new technique offers higher mass-resolving power, allows checking for the presence of contaminant ion species, and it proved useful in tuning the harmonicity of the trapping potential as well as in aligning the trap symmetry axis with respect to the magnetic field axis by visualizing the radial ion motion. This is a non-scanning technique where every detected ion contributes equally, therefore it is more sensitive than the previously used time-of-flight ion-cyclotron-resonance (ToF-ICR) technique, which is based on the scanning of the sideband-frequency of trapped ions and recording their time of flight after ejection. It will enable us to carry out high-precision mass measurements in the actinide region with uncertainties on the ppb level.

Brho -defined isochronous mass spectrometry and mass measurements of ^{58}Ni fragments

A novel isochronous mass spectrometry, termed as Brho -defined IMS, has been established at the experimental cooler-storage ring CSRe in Lanzhou. Its potential has been studied through high precision mass measurements of ^{58}Ni projectile fragments. Two time-of-flight detectors were installed in one of the straight sections of CSRe, thus enabling simultaneous measurements of the velocity and the revolution time of each stored short-lived ion. This allows for calculating the magnetic rigidity Brho and the orbit length C of each ion. The accurate Brho (C) function has been constructed, which is a universal calibration curve used to deduce the masses of the stored nuclides. The sensitivity to single stored ions, fast measurement time, and background-free characteristics of the method are ideally suited to address nuclides with very short lifetimes and smallest production yields. In the limiting case of just a single particle, the achieved mass resolving power allows one to determine its mass-over-charge ratio m/q with a remarkable precision of merely sim 5 keV. Masses of T_z=-3/2fp-shell nuclides are re-determined with high accuracy, and the validity of the isospin multiplet mass equation is tested up to the heaviest isospin quartet with A=55. The new masses are also used to investigate the mirror symmetry of empirical residual proton-neutron interactions.

Study of the N=32 and N=34 Shell Gap for Ti and V by the First High-Precision Multireflection Time-of-Flight Mass Measurements at BigRIPS-SLOWRI.

The atomic masses of ^{55}Sc, ^{56,58}Ti, and ^{56-59}V have been determined using the high-precision multireflection time-of-flight technique. The radioisotopes have been produced at RIKEN's Radioactive Isotope Beam Factory (RIBF) and delivered to the novel designed gas cell and multireflection system, which has been recently commissioned downstream of the ZeroDegree spectrometer following the BigRIPS separator. For ^{56,58}Ti and ^{56-59}V, the mass uncertainties have been reduced down to the order of 10keV, shedding new light on the N=34 shell effect in Ti and V isotopes by the first high-precision mass measurements of the critical species ^{58}Ti and ^{59}V. With the new precision achieved, we reveal the nonexistence of the N=34 empirical two-neutron shell gaps for Ti and V, and the enhanced energy gap above the occupied νp_{3/2} orbit is identified as a feature unique to Ca. We perform new MonteCarlo shell model calculations including the νd_{5/2} and νg_{9/2} orbits and compare the results with conventional shell model calculations, which exclude the νg_{9/2} and the νd_{5/2} orbits. The comparison indicates that the shell gap reduction in Ti is related to a partial occupation of the higher orbitals for the outer two valence neutrons at N=34.

Bρ -defined isochronous mass spectrometry: An approach for high-precision mass measurements of short-lived nuclei

A novel technique for broadband high-precision mass measurements of short-lived exotic nuclides is reported. It is based on the isochronous mass spectrometry (IMS) and realizes simultaneous determinations of revolution time and velocity of short-lived stored ions at the cooler storage ring CSRe in Lanzhou. The new technique, named as the $B\rho$-defined IMS or $B\rho$-IMS, boosts the efficiency, sensitivity, and accuracy of mass measurements, and is applied here to measure masses of neutron-deficient $fp$-shell nuclides. In a single accelerator setting, masses of $^{46}$Cr, $^{50}$Fe and $^{54}$Ni are determined with relative uncertainties of (5~-~6)$\times10^{-8}$, thereby improving the input data for testing the unitarity of the Cabibbo-Kobayashi-Maskawa quark mixing matrix. This is the technique of choice for future high-precision measurements of the most rarely produced shortest-lived nuclides.

Development of a mass spectrometer for high-precision mass measurements of superheavy elements at JINR

A multiple-reflection time-of-flight (MR TOF) mass spectrometer for mass measurements of superheavy elements is currently being developed for an experimental cave of the Superheavy Element Factory at the Joint Institute for Nuclear Research in Dubna. Its conceptual and ion-optical designs are described in the present paper. The spectrometer is designed to achieve a mass measurement accuracy of 10^-7 at low measurement statistics (~5 events) for nuclides with half-lives down to 50 ms. To reach this goal, a new generation MR TOF analyzer with an ultra-high mass resolving power and highly-stable power supplies has been designed. An advanced set of ion-optical solutions for preparation and mass separation of the sample and calibrant ion beams is proposed for the spectrometer: a radiofrequency multiplexer trap separator of charge states, high vacuum quadrupole filters with two-stage differential pumping, operated in the “beat node coincidence” mode, a focused beam transport through the gate valve gaps, as well as a fullerene soot electron ionization calibrant ion source.

Impact of nuclear mass measurements in the vicinity of 132Sn on the r-process nucleosynthesis

Nuclear masses are a key aspect in the modelling of nuclear reaction rates for the r-process nucleosynthesis. High precision mass measurements drastically reduce the associated uncertainties in the modelling of r-process nucleosynthesis. We investigate the impact of nuclear mass uncertainties on neutron-capture rates calculations using a Hauser – Feshbach statistical code in the vicinity of 132Sn. Finally, we study the impact of the propagated neutron-capture reaction rates uncertainties on the r-process nucleosynthesis. We find that mass measurements with uncertainties higher than 20 keV affect the calculation of reaction rates. We also note that modelling of reaction rates can differ for more than a factor of two even for experimentally known nuclear masses.

Investigating nuclear structure near N=32 and N=34: Precision mass measurements of neutron-rich Ca, Ti, and V isotopes

Nuclear mass measurements of isotopes are key to improving our understanding of nuclear structure across the chart of nuclides, in particular for the determination of the appearance or disappearance of nuclear shell closures. We present high-precision mass measurements of neutron-rich Ca, Ti and V isotopes performed at the TITAN and LEBIT facilities. These measurements were made using the TITAN multiple-reflection time-of-flight mass spectrometer (MR-ToF-MS) and the LEBIT 9.4T Penning trap mass spectrometer. In total, 13 masses were measured, eight of which represent increases in precision over previous measurements. These measurements refine trends in the mass surface around $N = 32$ and $N = 34$, and support the disappearance of the $N = 32$ shell closure with increasing proton number. Additionally, our data does not support the presence of a shell closure at $N = 34$.

Mass measurements towards doubly magic 78Ni: Hydrodynamics versus nuclear mass contribution in core-collapse supernovae

We report the first high-precision mass measurements of the neutron-rich nuclei 74,75Ni and the clearly identified ground state of 76Cu, along with a more precise mass-excess value of 78Cu, performed with the double Penning trap JYFLTRAP at the Ion Guide Isotope Separator On-Line (IGISOL) facility. These new results lead to a quantitative estimation of the quenching for the N=50 neutron shell gap. The impact of this shell quenching on core-collapse supernova dynamics is specifically tested using a dedicated statistical equilibrium approach that allows a variation of the mass model independent of the other microphysical inputs. We conclude that the impact of nuclear masses is strong when implemented using a fixed trajectory as in the previous studies, but the effect is substantially reduced when implemented self-consistently in the simulation.