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Title: Fluctuations in cool quark matter and the phase diagram of quantum chromodynamics

Abstract

Here, we consider the phase diagram of hadronic matter as a function of temperature,T, and baryon chemical potential, μ. Currently the dominant paradigm is a line of first order transitions which ends at a critical endpoint.

Authors:
; ;
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1509773
Alternate Identifier(s):
OSTI ID: 1504875
Report Number(s):
BNL-211498-2019-JAAM
Journal ID: ISSN 2470-0010; PRVDAQ; 074025
Grant/Contract Number:  
SC0012704
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 99 Journal Issue: 7; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Pisarski, Robert D., Skokov, Vladimir V., and Tsvelik, Alexei M. Fluctuations in cool quark matter and the phase diagram of quantum chromodynamics. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.99.074025.
Pisarski, Robert D., Skokov, Vladimir V., & Tsvelik, Alexei M. Fluctuations in cool quark matter and the phase diagram of quantum chromodynamics. United States. doi:10.1103/PhysRevD.99.074025.
Pisarski, Robert D., Skokov, Vladimir V., and Tsvelik, Alexei M. Mon . "Fluctuations in cool quark matter and the phase diagram of quantum chromodynamics". United States. doi:10.1103/PhysRevD.99.074025.
@article{osti_1509773,
title = {Fluctuations in cool quark matter and the phase diagram of quantum chromodynamics},
author = {Pisarski, Robert D. and Skokov, Vladimir V. and Tsvelik, Alexei M.},
abstractNote = {Here, we consider the phase diagram of hadronic matter as a function of temperature,T, and baryon chemical potential, μ. Currently the dominant paradigm is a line of first order transitions which ends at a critical endpoint.},
doi = {10.1103/PhysRevD.99.074025},
journal = {Physical Review D},
number = 7,
volume = 99,
place = {United States},
year = {2019},
month = {4}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.99.074025

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Cited by: 3 works
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margin-top:0px;">Works referencing / citing this record:</p> <div class="list"> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/physrevd.101.054032" target="_blank" rel="noopener noreferrer" class="name">QCD phase structure at finite temperature and density<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2020-03-01">March 2020</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Fu, Wei-jie; Pawlowski, Jan M.; Rennecke, Fabian</span> </li> <li> Physical Review D, Vol. 101, Issue 5</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1103/physrevd.101.054032" class="text-muted" target="_blank" rel="noopener noreferrer">10.1103/physrevd.101.054032<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> </div> <div class="pagination-container small"> <a class="pure-button prev page" href="#" rel="prev"><span class="fa fa-angle-left"></span></a><ul class="pagination d-inline-block" style="padding-left:.2em;"></ul><a class="pure-button next page" href="#" rel="next"><span class="fa fa-angle-right"></span></a> </div> </div> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a href="" class="reference-type-filter tab-nav" data-filter="type" data-pattern="*"><span class="fa fa-angle-right"></span> All Cited By</a></li> <li class="small" style="margin-left:.75em; 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float:none;">[ × clear filter / sort ]</a> </div> </form> </div> </div> </div> </section> <section id="biblio-related" class="tab-content tab-content-sec " data-tab="biblio"> <div class="row"> <div class="col-sm-9 order-sm-9"> <section id="biblio-similar" class="tab-content tab-content-sec active" data-tab="related"> <div class="padding"> <p class="lead text-muted" style="font-size: 18px; margin-top:0px;">Similar Records in DOE PAGES and OSTI.GOV collections:</p> <aside> <ul class="item-list" itemscope itemtype="http://schema.org/ItemList" style="padding-left:0; list-style-type: none;"> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="1" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/pages/biblio/1598592-indications-critical-end-point-phase-diagram-hot-dense-nuclear-matter" itemprop="url">Indications for a Critical End Point in the Phase Diagram for Hot and Dense Nuclear Matter</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Lacey, Roy A.</span> <span class="text-muted pubdata"> - Physical Review Letters</span> </span> </div> <div class="abstract">Here, exci<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> tation functions for the Gaussian emission source radii difference ( <math> <msubsup> <mi> R </mi> <mtext> out </mtext> <mn> 2 </mn> </msubsup><mo> - </mo><msubsup> <mi> R </mi> <mtext> side </mtext> <mn> 2 </mn> </msubsup> </math>) obtained from two-pion interferometry measurements in <math> <mi> Au </mi><mo> + </mo><mi> Au </mi> </math> ( <math> <mrow> <msqrt> <mrow> <msub> <mrow> <mi> s </mi> </mrow> <mrow> <mi> N </mi> <mi> N </mi> </mrow> </msub> </mrow> </msqrt> <mo> = </mo> <mn> 7.7 </mn> <mi> – </mi> <mn> 200 </mn> <mtext></mtext> <mtext></mtext> <mi> GeV </mi> </mrow> </math>) and <math> <mi> Pb </mi><mo> + </mo><mi> Pb </mi> </math> ( <math> <mrow> <msqrt> <mrow> <msub> <mrow> <mi> s </mi> </mrow> <mrow> <mi> N </mi> <mi> N </mi> </mrow> </msub> </mrow> </msqrt> <mo> = </mo> <mn> 2.76 </mn> <mtext></mtext> <mtext></mtext> <mi> TeV </mi> </mrow> </math>) collisions are reported on for a broad range of collision centralities. The observed nonmonotonic excitation functions validate the finite-size scaling patterns expected for the deconfinement phase transition and the critical end point (CEP), in the temperature versus baryon chemical potential ( <math> <mi> T </mi><mo> , </mo><msub> <mi> μ </mi> <mi> B </mi> </msub> </math>) plane of the nuclear matter phase diagram. A finite-size scaling (FSS) analysis of these data suggests a second order phase transition with the estimates <math> <mrow> <msup> <mrow> <mi> T </mi> </mrow> <mrow> <mi> cep </mi> </mrow> </msup> <mo> ~ </mo> <mn> 165 </mn> <mtext></mtext> <mtext></mtext> <mi> MeV </mi> </mrow> </math> and <math> <msubsup> <mi> μ </mi> <mi> B </mi> <mi> cep </mi> </msubsup><mo> ~ </mo><mn> 95 </mn><mtext></mtext><mtext></mtext><mi> MeV </mi> </math> for the location of the critical end point. The critical exponents ( <math> <mi> ν </mi><mo> ≈ </mo><mn> 0.66 </mn> </math> and <math> <mi> γ </mi><mo> ≈ </mo><mn> 1.2 </mn> </math>) extracted via the same FSS analysis place this CEP in the 3D Ising model universality class.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 38<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink">DOI: <a class="misc doi-link " href="https://doi.org/10.1103/PhysRevLett.114.142301" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1598592" data-product-type="Journal Article" data-product-subtype="AM" >10.1103/PhysRevLett.114.142301</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/pages/servlets/purl/1598592" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1598592" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="3" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/pages/biblio/1437871-light-nuclei-production-probe-qcd-phase-diagram" itemprop="url">Light nuclei production as a probe of the QCD phase diagram</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Sun, Kai-Jia</span> ; <span class="author">Chen, Lie-Wen</span> ; <span class="author">Ko, Che Ming</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - Physics Letters B</span> </span> </div> <div class="abstract">It is generally believed that the quark-hadron transition at small values of baryon chemical potentials µ<sub>B</sub> is a crossover but changes to a first-order phase transition with an associated critical endpoint (CEP) as µ<sub>B</sub> increases. Such a µ<sub>B</sub>-dependent quark-hadron transition is expected to result in a double-peak structure in the collision energy dependence of the baryon density fluctuation in heavy-ion collisions with one at lower energy due to the spinodal instability during the first-order phase transition and another at higher energy due to the critical fluctuations in the vicinity of the CEP. By analyzing the data on the p, d and <sup>3</sup>H yields in central heavy-ion collisions within the coalescence model for light nuclei production, we find that the relative neutron density fluctuation Δρ<sub>n</sub> =<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> $$\langle$$(δρ<sub>n</sub>)<sup>2</sup>$$\rangle$$/$$\langle$$ρn<sup>2</sup>$$\rangle$$ at kinetic freeze-out indeed displays a clear peak at $$\sqrt{s}$$$_ {NN}$$ = 8.8 GeV and a possible strong re-enhancement at $$\sqrt{s}$$$_ {NN}$$ = 4.86 GeV. Thus, our findings provide a strong support for the existence of a first-order phase transition at large µ<sub>B</sub> and its critical endpoint at a smaller µ<sub>B</sub> in the temperature versus baryon chemical potential plane of the QCD phase diagram.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 4<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink">DOI: <a class="misc doi-link " href="https://doi.org/10.1016/j.physletb.2018.04.035" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1437871" data-product-type="Journal Article" data-product-subtype="PA" >10.1016/j.physletb.2018.04.035</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="4" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/20774806-phase-diagram-neutral-quark-matter-nonlocal-chiral-quark-models" itemprop="url">Phase diagram of neutral quark matter in nonlocal chiral quark models</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Gomez Dumm, D Gomez</span> ; <span class="author">Gesellschaft fuer Schwerionenforschung</span> ; <span class="author">Blaschke, D B</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - Physical Review. D, Particles Fields</span> </span> </div> <div class="abstract">We consider the phase diagram of two-flavor quark matter under neutron star constraints for two nonlocal, covariant quark models within the mean-field approximation. In the first case (Model I) the nonlocality arises from the regularization procedure, motivated by the instanton liquid model, whereas in the second one (Model II) a separable approximation of the one-gluon exchange interaction is applied. We find that Model II predicts a larger quark mass gap and a chiral symmetry breaking (CSB) phase transition line which extends 15-20% further into the phase diagram spanned by temperature (T) and chemical potential ({mu}). The corresponding critical temperature at<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> {mu}=0, T{sub c}(0){approx_equal}140 MeV, is in better accordance to recent lattice QCD results than the prediction of the standard local NJL model, which exceeds 200 MeV. For both Model I and Model II we have considered various coupling strengths in the scalar diquark channel, showing that different low-temperature quark matter phases can occur at intermediate densities: a normal quark matter (NQM) phase, a two-flavor superconducting (2SC) quark matter phase and a mixed 2SC-NQM phase. Although in most cases there is also a gapless 2SC phase, this occurs in general in a small region at nonzero temperatures, thus its effect should be negligible for compact star applications.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink">DOI: <a class="misc doi-link " href="https://doi.org/10.1103/PhysRevD.73.114019" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="20774806" data-product-type="Journal Article" data-product-subtype="" >10.1103/PhysRevD.73.114019</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="5" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/20705920-heating-gapless-color-flavor-locked-quark-matter" itemprop="url">Heating (gapless) color-flavor locked quark matter</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Fukushima, Kenji</span> ; <span class="author">Kouvaris, Chris</span> ; <span class="author">Rajagopal, Krishna</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - Physical Review. D, Particles Fields</span> </span> </div> <div class="abstract">We explore the phase diagram of neutral quark matter at high baryon density as a function of the temperature T and the strange quark mass M{sub s}. At T=0, there is a sharp distinction between the insulating color-flavor locked (CFL) phase, which occurs where M{sub s}{sup 2}/{mu}<2{delta}, and the metallic gapless CFL phase, which occurs at larger M{sub s}{sup 2}/{mu}. Here, {mu} is the chemical potential for quark number and {delta} is the gap in the CFL phase. We find this distinction blurred at T{ne}0, as the CFL phase undergoes an insulator to metal crossover when it is heated. We<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> present an analytic treatment of this crossover. At higher temperatures, we map out the phase transition lines at which the gap parameters {delta}{sub 1}, {delta}{sub 2}, and {delta}{sub 3} describing ds pairing, us pairing and ud pairing, respectively, go to zero in an Nambu-Jona-Lasinio (NJL) model. For small values of M{sub s}{sup 2}/{mu}, we find that {delta}{sub 2} vanishes first, then {delta}{sub 1}, then {delta}{sub 3}. We find agreement with a previous Ginzburg-Landau analysis of the form of these transitions and find quantitative agreement with results obtained in full QCD at asymptotic density for ratios of coefficients in the Ginzburg-Landau potential. At larger M{sub s}{sup 2}/{mu}, we find that {delta}{sub 1} vanishes first, then {delta}{sub 2}, then {delta}{sub 3}. Hence, we find a ''doubly critical'' point in the (M{sub s}{sup 2}/{mu},T) plane at which two lines of second order phase transitions ({delta}{sub 1}{yields}0 and {delta}{sub 2}{yields}0) cross. Because we do not make any small-M{sub s} approximation, if we choose a relatively strong coupling leading to large gap parameters, we are able to pursue the analysis of the phase diagram all the way up to such large values of M{sub s} that there are no strange quarks present.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink">DOI: <a class="misc doi-link " href="https://doi.org/10.1103/PhysRevD.71.034002" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="20705920" data-product-type="Journal Article" data-product-subtype="" >10.1103/PhysRevD.71.034002</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="6" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/20933244-phase-diagram-finite-temperature-quark-density-strong-coupling-limit-lattice-qcd-color-su" itemprop="url">Phase diagram at finite temperature and quark density in the strong coupling limit of lattice QCD for color SU(3)</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Kawamoto, N</span> ; <span class="author">Miura, K</span> ; <span class="author">Ohnishi, A</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - Physical Review. D, Particles Fields</span> </span> </div> <div class="abstract">We study the phase diagram of quark matter at finite temperature (T) and chemical potential ({mu}) in the strong coupling limit of lattice QCD for color SU(3). We derive an analytical expression of the effective free energy as a function of T and {mu}, including baryon effects. The finite temperature effects are evaluated by integrating over the temporal link variable exactly in the Polyakov gauge with an antiperiodic boundary condition for fermions. The obtained phase diagram shows the first and the second order phase transition at low and high temperatures, respectively, and those are separated by the tricritical point in<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> the chiral limit. Baryon has effects to reduce the effective free energy and to extend the hadron phase to a larger {mu} direction at low temperatures.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink">DOI: <a class="misc doi-link " href="https://doi.org/10.1103/PHYSREVD.75.014502" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="20933244" data-product-type="Journal Article" data-product-subtype="" >10.1103/PHYSREVD.75.014502</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> </ul> </aside> </div> </section> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a class="tab-nav disabled" data-tab="related" style="color: #636c72 !important; opacity: 1;"><span class="fa fa-angle-right"></span> Similar Records</a></li> </ul> </div> </div> </section> </div></div> </div> </div> </section> <footer class="" style="background-color:#f9f9f9; /* padding-top: 0.5rem; */"> <div class="footer-minor"> <div class="container"> <hr class="footer-separator" /> <div class="text-center" style="margin-top:1.25rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list" id="footer-org-menu"> <li class="pure-menu-item"> <a href="https://energy.gov" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-us-doe-min" alt="U.S. Department of Energy" /> </a> </li> <li class="pure-menu-item"> <a href="https://www.energy.gov/science/office-science" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-office-of-science-min" alt="Office of Science" /> </a> </li> <li class="pure-menu-item"> <a href="/"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-osti-min" alt="Office of Scientific and Technical Information" /> </a> </li> </ul> </div> </div> <div class="text-center small" style="margin-top:0.5em;margin-bottom:2.0rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list"> <li class="pure-menu-item"><a href="/disclaim" class="pure-menu-link"><span class="fa fa-institution"></span> Website Policies <span class="hidden-xs">/ Important Links</span></a></li> <li class="pure-menu-item"><a href="/pages/contact" class="pure-menu-link"><span class="fa fa-comments-o"></span> Contact Us</a></li> <li class="d-block d-md-none"></li> <li class="pure-menu-item"><a href="https://www.facebook.com/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-facebook" style=""></span></a></li> <li class="pure-menu-item"><a href="https://twitter.com/OSTIgov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-twitter" style=""></span></a></li> <li class="pure-menu-item"><a href="https://www.youtube.com/user/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-youtube-play" style=""></span></a></li> </ul> </div> </div> </div> </div> </footer> <link href="/pages/css/pages.fonts.200912.1307.css" rel="stylesheet"> <script src="/pages/js/pages.200912.1307.js"></script><noscript></noscript> <script defer src="/pages/js/pages.biblio.200912.1307.js"></script><noscript></noscript> <script defer src="/pages/js/lity.js"></script><noscript></noscript> <script async type="text/javascript" src="/pages/js/Universal-Federated-Analytics-Min.js?agency=DOE" id="_fed_an_ua_tag"></script><noscript></noscript> </body> <!-- DOE PAGES v.200912.1307 --> </html>