* Weak U.S. payrolls, PMI reports in Europe, spell gloom * Global shares slide; bond prices jump on QE3 hopes * Brent crude falls to 3-month lows under $113 a barrel * Dollar slips vs yen in volatile trade, euro weakens By Herbert Lash NEW YORK, May 4 (Reuters) - Global stocks swooned and crude oil tumbled on Friday after a weak U.S. jobs report and economic data that pointed to a deeper recession across the euro zone than previously thought. Major U.S. and European stock indexes fell more than 1 percent, crude oil slumped about 4 percent and government debt prices jumped after the Labor Department said U.S. employers cut back on hiring in April more than expected. Employers added just 115,000 workers to payrolls last month, or 55,000 less than economists expected. The unemployment rate fell one-tenth of a point to 8.1 percent, a three-year low, but only because the workforce shrank as people retired or stopped looking for a job. The third straight monthly decline in hiring growth spurred concerns that the U.S. economy is losing momentum and doused hopes that a stretch of strong winter hiring had signaled a turning point for the U.S. recovery. "The U.S. economy is not growing fast enough to improve the job market. When all is said and done that is the most important statistic," said Joseph Trevisani, chief market strategist at Worldwide Markets in Woodcliff Lake, New Jersey. The Dow Jones industrial average was down 164.16 points, or 1.24 percent, at 13,042.43. The Standard & Poor's 500 Index was down 21.27 points, or 1.53 percent, at 1,370.30. The Nasdaq Composite Index was down 58.14 points, or 1.92 percent, at 2,966.16. The U.S. jobs data added to the gloomy tone from Europe, where purchasing managers' indexes, primarily covering services, suggested a recession across the euro zone could extend to mid-year and be deeper than previously thought. Markit's Eurozone Services PMI, which gauges business activity over a month, came in at 46.9 for April, sharply lower than 49.2 in March. Anything below 50 signifies contraction. The JPMorgan Global Purchasing All-Industry Output Index of about 20 countries showed declines in April from March. In Europe, the pan-European FTSEurofirst 300 index closed down 1.7 percent to 1,027.15 points, and the Euro STOXX 50 index fell 1.7 percent to 2,249.27, despite strong corporate earnings from Royal Bank of Scotland, BNP Paribas and Lafarge. MSCI's all-country world equity index fell 1.5 percent to 321.58. Some analysts said the jobs report, which followed weaker-than-expected services sector data this week, will fuel expectations of a third round of stimulus, or quantitative easing, by the Federal Reserve to keep rates low and foster growth. "The headline disappointment increases the likelihood that (Fed Chairman Ben) Bernanke will move forward with QE3 later this summer in an attempt to further bolster employment growth," said Michael Woolfolk, senior currency strategist at BNY Mellon in New York. The dollar slipped against the yen in volatile trading after the payrolls number, with the U.S. currency down 0.41 percent at 79.86 yen. The U.S. dollar index rose 0.37 percent at 79.512. The euro was down 0.43 percent at $1.3094. The benchmark 10-year U.S. Treasury note rose 15/32 in price to yield 1.88 percent, and the 30-year U.S. Treasury bond gained 25/32 in price to yield 3.08 percent. Oil fell to three-month lows around $112 a barrel, on course for its steepest weekly fall since December, after the weak U.S. jobs report. Brent crude oil futures lost $3.80 to $112.28 a barrel, lows last seen in early February. U.S. crude fell $4.51 to $98.03 a barrel. "We are locked in this sluggish growth environment," said Robert Vanden Assem, head of investment grade fixed income at PineBridge Investments in New York, which manages about $67 billion in assets.